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## Schilling, René Leander

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 Author ID: schilling.rene-leander Published as: Schilling, René L.; Schilling, R. L.; Schilling, Rene L.; Schilling, René; Schilling, René Leander; Schilling, R. External Links: MGP
 Documents Indexed: 103 Publications since 1994, including 15 Books Reviewing Activity: 233 Reviews
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#### Co-Authors

 21 single-authored 13 Jacob, Niels 12 Wang, Jian 7 Böttcher, Björn 7 Deng, Changsong 7 Knopova, Victoria Pavlovna 7 Lindner, Felix 5 Cioica, Petru A. 5 Dahlke, Stephan 5 Kinzel, Stefan 5 Kühn, Franziska 5 Raasch, Thorsten 5 Ritter, Klaus 4 Kinderknecht, Yana A. 4 Döhring, Nicolas 4 Smolyanov, Oleg Georgievich 3 Meerschaert, Mark Marvin 3 Vondraček, Zoran 2 Burdzy, Krzysztof 2 Farkas, Walter 2 Friedrich, Ulrich 2 Keller-Ressel, Martin 2 Khoshnevisan, Davar 2 Kolokoltsov, Vassili N. 2 Kovács, Mihály 2 Kulczycki, Tadeusz 2 Partzsch, Lothar 2 Porcu, Emilio 2 Sikorskii, Alla 2 Song, Renming 2 Song, Yanhong 2 Uemura, Toshihiro 1 Bäumer, Boris 1 Bereyhi, M. J. 1 Engelsen, N. J. 1 Fedorov, S. A. 1 Germano, Guido 1 Ghadimi, A. H. 1 Kaleta, Kamil 1 Kippenberg, T. J. 1 Landwehr, Sandra 1 Leonenko, Nikolai N. 1 Liang, Mingjie 1 Lifshits, Mikhail A. 1 Magdziarz, Marcin 1 Mimica, Ante 1 Mishura, Yuliya Stepanivna 1 Politi, Mauro 1 Sandrić, Nikola 1 Scalas, Enrico 1 Schnurr, Alexander 1 Straka, Peter 1 Sztonyk, Paweł 1 Tyukov, Alexei E. 1 Tyurin, Ilya 1 Xiao, Yimin
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#### Serials

 5 Stochastic Processes and their Applications 4 Bernoulli 4 De Gruyter Studium 3 Transactions of the American Mathematical Society 3 Journal of Theoretical Probability 3 Potential Analysis 3 Electronic Journal of Probability 2 Advances in Applied Probability 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Zeitschrift für Analysis und ihre Anwendungen 2 Statistics & Probability Letters 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 Expositiones Mathematicae 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 De Gruyter Studies in Mathematics 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Studia Mathematica 1 The Annals of Statistics 1 BIT 1 Bulletin of the London Mathematical Society 1 Dissertationes Mathematicae 1 Integral Equations and Operator Theory 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Publicationes Mathematicae 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tohoku Mathematical Journal. Second Series 1 Probability and Mathematical Statistics 1 Stochastic Analysis and Applications 1 Acta Applicandae Mathematicae 1 Probability Theory and Related Fields 1 Journal of the Australian Mathematical Society. Series A 1 Stochastics and Stochastics Reports 1 Russian Journal of Mathematical Physics 1 Electronic Communications in Probability 1 Doklady Mathematics 1 Nonlinear Dynamics 1 Positivity 1 Fractional Calculus & Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Evolution Equations 1 Foundations of Computational Mathematics 1 Stochastics and Dynamics 1 Mediterranean Journal of Mathematics 1 Lecture Notes in Mathematics 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Science 1 Science China. Mathematics 1 Communications in Applied and Industrial Mathematics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Modern Stochastics. Theory and Applications 1 Advanced Courses in Mathematics – CRM Barcelona 1 De Gruyter Textbook 1 De Gruyter Graduate
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#### Fields

 87 Probability theory and stochastic processes (60-XX) 28 Operator theory (47-XX) 24 Partial differential equations (35-XX) 15 Potential theory (31-XX) 9 Measure and integration (28-XX) 8 Numerical analysis (65-XX) 7 Functional analysis (46-XX) 4 Real functions (26-XX) 4 Statistics (62-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH Open

88 Publications have been cited 1,126 times in 680 Documents Cited by Year
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
Growth and Hölder conditions for the sample paths of Feller processes. Zbl 0930.60013
Schilling, René L.
1998
Lévy matters III. Lévy-type processes: construction, approximation and sample path properties. Zbl 1384.60004
Böttcher, Björn; Schilling, René; Wang, Jian
2013
A note on the existence of transition probability densities of Lévy processes. Zbl 1269.60050
Knopova, Victoria; Schilling, René L.
2013
Coupling property and gradient estimates of Lévy processes via the symbol. Zbl 1263.60045
Schilling, René L.; Sztonyk, Paweł; Wang, Jian
2012
The symbol associated with the solution of a stochastic differential equation. Zbl 1226.60116
Schilling, Rene L.; Schnurr, Alexander
2010
Conservativeness and extensions of Feller semigroups. Zbl 0919.47033
Schilling, René L.
1998
Lévy-type processes and pseudodifferential operators. Zbl 0984.60054
Jacob, Niels; Schilling, René L.
2001
Subordination in the sense of Bochner and a related functional calculus. Zbl 0920.47039
Schilling, René L.
1998
Function spaces related to continuous negative definite functions: $$\psi$$-Bessel potential spaces. Zbl 0990.46018
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Measures, integrals and martingales. Zbl 1084.28001
Schilling, René L.
2005
On the Feller property of Dirichlet forms generated by pseudo differential operators. Zbl 1141.31006
Schilling, René L.; Uemura, Toshihiro
2007
Asymptotic properties of Brownian motion delayed by inverse subordinators. Zbl 1329.60291
Magdziarz, Marcin; Schilling, René L.
2015
Transition density estimates for a class of Lévy and Lévy-type processes. Zbl 1242.60082
Knopova, Viktorya; Schilling, René L.
2012
Correlation structure of time-changed Lévy processes. Zbl 1329.60118
Leonenko, Nikolai N.; Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2014
A geometric interpretation of the transition density of a symmetric Lévy process. Zbl 1279.60097
Jacob, Niels; Knopova, Victorya; Landwehr, Sandra; Schilling, René L.
2012
On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes. Zbl 1247.60113
Schilling, René L.; Wang, Jian
2012
On the coupling property of Lévy processes. Zbl 1268.60061
Schilling, René L.; Wang, Jian
2011
Approximation of Feller processes by Markov chains with Lévy increments. Zbl 1168.60359
Böttcher, Björn; Schilling, René L.
2009
Constructions of coupling processes for Lévy processes. Zbl 1217.60035
Böttcher, Björn; Schilling, René L.; Wang, Jian
2011
Some theorems on Feller processes: transience, local times and ultracontractivity. Zbl 1282.60070
Schilling, René L.; Wang, Jian
2013
Strong Feller continuity of Feller processes and semigroups. Zbl 1258.60047
Schilling, René L.; Wang, Jian
2012
On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes. Zbl 1328.60118
Deng, Chang-Song; Schilling, René L.
2015
Weak order for the discretization of the stochastic heat equation driven by impulsive noise. Zbl 1263.60058
Lindner, Felix; Schilling, René L.
2013
Reflected spectrally negative stable processes and their governing equations. Zbl 1378.60075
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Schilling, René L.; Straka, Peter
2016
Functional inequalities and subordination: Stability of Nash and Poincaré inequalities. Zbl 1259.47058
Schilling, René L.; Wang, Jian
2012
Some Dirichlet spaces obtained by subordinate reflected diffusions. Zbl 0922.31011
Jacob, Niels; Schilling, René L.
1999
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070
Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G.
2012
Function spaces as path spaces of Feller processes. Zbl 0970.60043
Schilling, René L.
2000
Feynman formulae for Feller semigroups. Zbl 1213.47047
Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L.
2010
Feller processes generated by pseudo-differential operators: On the Hausdorff dimension of their sample paths. Zbl 0910.60028
Schilling, René L.
1998
Conservativeness of semigroups generated by pseudo differential operators. Zbl 0917.60066
Schilling, René L.
1998
Brownian motion. An introduction to stochastic processes. With contributions by Björn Böttcher. 2nd revised and extended ed. Zbl 1283.60003
Schilling, René L.; Partzsch, Lothar
2014
On Feller processes with sample paths in Besov spaces. Zbl 0888.60036
Schilling, René L.
1997
Feller semigroup, $$L^p$$-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. Zbl 0978.47031
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Stochastic solutions for fractional wave equations. Zbl 1345.35134
Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2015
Measures, integrals and martingales. 2nd edition. Zbl 1360.28001
Schilling, René L.
2017
Function spaces as Dirichlet spaces (about a paper by Maz’ya and Nagel). Zbl 1107.46027
Jacob, Niels; Schilling, René L.
2005
Brownian motion. An introduction to stochastic processes. With a chapter on simulation by Björn Böttcher. Zbl 1258.60002
Schilling, René L.; Partzsch, Lothar
2012
Towards an $$L^p$$ potential theory for sub-Markovian semigroups: kernels and capacities. Zbl 1104.31007
Jacob, Niels; Schilling, René L.
2006
From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class. Zbl 1280.60032
Porcu, Emilio; Schilling, René L.
2011
On the domain of fractional Laplacians and related generators of Feller processes. Zbl 1464.60044
Kühn, Franziska; Schilling, René L.
2019
Lower bounded semi-Dirichlet forms associated with Lévy type operators. Zbl 1336.31030
Schilling, René L.; Wang, Jian
2015
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Zbl 1250.60026
Cioica, Petru A.; Dahlke, Stephan; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2011
On the structure of the domain of a symmetric jump-type Dirichlet form. Zbl 1241.31013
Schilling, René L.; Uemura, Toshihiro
2012
Feynman formulas and path integrals for some evolution semigroups related to $$\tau$$-quantization. Zbl 1311.58006
Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G.
2011
Packing dimension profiles and Lévy processes. Zbl 1266.60071
Khoshnevisan, D.; Schilling, R. L.; Xiao, Y.
2012
An analytic proof of the Lévy-Khinchin formula on $$R^n$$. Zbl 0928.42003
Jacob, Niels; Schilling, René L.
1998
Adaptive wavelet methods for the stochastic Poisson equation. Zbl 1260.65003
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2012
Dirichlet operators and the positive maximum principle. Zbl 0994.31003
Schilling, Rene L.
2001
On the domain of the generator of a subordinate semigroup. Zbl 0857.47025
Schilling, René L.
1996
Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114
Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G.
2011
From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet. Zbl 1382.60005
Khoshnevisan, Davar; Schilling, René
2016
Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs. Zbl 1422.60097
Kühn, Franziska; Schilling, René L.
2019
On the path behavior of Markov processes comparable with Lévy processes. (Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy-Prozessen vergleichbar sind.) Zbl 0805.60032
Schilling, René Leander
1994
Sobolev embedding for stochastic processes. Zbl 0970.60044
Schilling, René L.
2000
Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise. Zbl 1335.60131
Kovács, Mihály; Lindner, Felix; Schilling, René L.
2015
Convergence analysis of spatially adaptive Rothe methods. Zbl 1309.65107
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Friedrich, Ulrich; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form. Zbl 0970.31008
Jacob, N.; Schilling, R. L.
2000
A note on invariant sets. Zbl 1077.47045
Schilling, René L.
2004
On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion. Zbl 1329.60289
Deng, Chang-Song; Schilling, René L.
2015
Lower bounds of the Hausdorff dimension for the images of Feller processes. Zbl 1351.60043
Knopova, V.; Schilling, R. L.; Wang, J.
2015
A probabilistic inequality related to negative definite functions. Zbl 1270.60030
Lifshits, Mikhail; Schilling, René L.; Tyurin, Ilya
2013
Subgeometric rates of convergence for Markov processes under subordination. Zbl 1425.60064
Deng, Chang-Song; Schilling, René L.; Song, Yan-Hong
2017
Distance multivariance: new dependence measures for random vectors. Zbl 1467.62104
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2019
A unified approach to coupling SDEs driven by Lévy noise and some applications. Zbl 1465.60039
Liang, Mingjie; Schilling, René L.; Wang, Jian
2020
Comparable processes and the Hausdorff dimension of their sample paths. Zbl 0888.60035
Schilling, René L.
1996
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
Subordination in the sense of S. Bochner – An approach through pseudo differential operators. Zbl 0923.47023
Jacob, Niels; Schilling, René L.
1996
Estimates for Feller semigroups generated by pseudodifferential operators. Zbl 0931.35204
Jacob, Niels; Schilling, René L.
1996
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
Harnack inequalities for SDEs driven by time-changed fractional Brownian motions. Zbl 1386.60147
Deng, Chang-Song; Schilling, René L.
2017
On the small-time behaviour of Lévy-type processes. Zbl 1309.60027
Knopova, Victoria; Schilling, René L.
2014
On level and collision sets of some Feller processes. Zbl 1351.60044
Knopova, Victoria; Schilling, René L.
2015
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process. Zbl 1359.60054
Schilling, René L.; Vondraček, Zoran
2017
A probabilistic proof of Schoenberg’s theorem. Zbl 07053199
Kühn, Franziska; Schilling, René L.
2019
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance. Zbl 1417.62158
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2018
When does a càdlàg process have continuous sample paths? Zbl 0830.60036
Schilling, René L.
1994
On a Poincaré-type inequality for energy forms in $$L^p$$. Zbl 1150.31003
Jacob, Niels; Schilling, René L.
2007
Elastic strain engineering for ultralow mechanical dissipation. Zbl 1416.81216
Ghadimi, A. H.; Fedorov, S. A.; Engelsen, N. J.; Bereyhi, M. J.; Schilling, R.; Wilson, D. J.; Kippenberg, T. J.
2018
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of stochastic partial differential equations. Zbl 1337.60160
Cioica, P. A.; Dahlke, S.; Döhring, N.; Friedrich, U.; Kinzel, S.; Lindner, F.; Raasch, T.; Ritter, K.; Schilling, René L.
2016
Adaptive wavelet methods for SPDEs. Zbl 1317.60084
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
Stationary distributions for jump processes with inert drift. Zbl 1291.60170
Burdzy, K.; Kulczycki, T.; Schilling, R. L.
2013
Correction to: “Subgeometric rates of convergence for Markov processes under subordination”. Zbl 1430.60062
Deng, C.-S.; Schilling, R. L.; Song, Y.-H.
2018
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
2019
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators. Zbl 07210214
Kaleta, Kamil; Schilling, René L.
2020
A unified approach to coupling SDEs driven by Lévy noise and some applications. Zbl 1465.60039
Liang, Mingjie; Schilling, René L.; Wang, Jian
2020
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators. Zbl 07210214
Kaleta, Kamil; Schilling, René L.
2020
On the domain of fractional Laplacians and related generators of Feller processes. Zbl 1464.60044
Kühn, Franziska; Schilling, René L.
2019
Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs. Zbl 1422.60097
Kühn, Franziska; Schilling, René L.
2019
Distance multivariance: new dependence measures for random vectors. Zbl 1467.62104
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2019
A probabilistic proof of Schoenberg’s theorem. Zbl 07053199
Kühn, Franziska; Schilling, René L.
2019
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
2019
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance. Zbl 1417.62158
Böttcher, Björn; Keller-Ressel, Martin; Schilling, René L.
2018
Elastic strain engineering for ultralow mechanical dissipation. Zbl 1416.81216
Ghadimi, A. H.; Fedorov, S. A.; Engelsen, N. J.; Bereyhi, M. J.; Schilling, R.; Wilson, D. J.; Kippenberg, T. J.
2018
Correction to: “Subgeometric rates of convergence for Markov processes under subordination”. Zbl 1430.60062
Deng, C.-S.; Schilling, R. L.; Song, Y.-H.
2018
Measures, integrals and martingales. 2nd edition. Zbl 1360.28001
Schilling, René L.
2017
Subgeometric rates of convergence for Markov processes under subordination. Zbl 1425.60064
Deng, Chang-Song; Schilling, René L.; Song, Yan-Hong
2017
Harnack inequalities for SDEs driven by time-changed fractional Brownian motions. Zbl 1386.60147
Deng, Chang-Song; Schilling, René L.
2017
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process. Zbl 1359.60054
Schilling, René L.; Vondraček, Zoran
2017
Reflected spectrally negative stable processes and their governing equations. Zbl 1378.60075
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Schilling, René L.; Straka, Peter
2016
From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet. Zbl 1382.60005
Khoshnevisan, Davar; Schilling, René
2016
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of stochastic partial differential equations. Zbl 1337.60160
Cioica, P. A.; Dahlke, S.; Döhring, N.; Friedrich, U.; Kinzel, S.; Lindner, F.; Raasch, T.; Ritter, K.; Schilling, René L.
2016
Asymptotic properties of Brownian motion delayed by inverse subordinators. Zbl 1329.60291
Magdziarz, Marcin; Schilling, René L.
2015
On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes. Zbl 1328.60118
Deng, Chang-Song; Schilling, René L.
2015
Stochastic solutions for fractional wave equations. Zbl 1345.35134
Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2015
Lower bounded semi-Dirichlet forms associated with Lévy type operators. Zbl 1336.31030
Schilling, René L.; Wang, Jian
2015
Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise. Zbl 1335.60131
Kovács, Mihály; Lindner, Felix; Schilling, René L.
2015
On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion. Zbl 1329.60289
Deng, Chang-Song; Schilling, René L.
2015
Lower bounds of the Hausdorff dimension for the images of Feller processes. Zbl 1351.60043
Knopova, V.; Schilling, R. L.; Wang, J.
2015
On level and collision sets of some Feller processes. Zbl 1351.60044
Knopova, Victoria; Schilling, René L.
2015
Correlation structure of time-changed Lévy processes. Zbl 1329.60118
Leonenko, Nikolai N.; Meerschaert, Mark M.; Schilling, René L.; Sikorskii, Alla
2014
Brownian motion. An introduction to stochastic processes. With contributions by Björn Böttcher. 2nd revised and extended ed. Zbl 1283.60003
Schilling, René L.; Partzsch, Lothar
2014
Convergence analysis of spatially adaptive Rothe methods. Zbl 1309.65107
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Friedrich, Ulrich; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
On the small-time behaviour of Lévy-type processes. Zbl 1309.60027
Knopova, Victoria; Schilling, René L.
2014
Adaptive wavelet methods for SPDEs. Zbl 1317.60084
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2014
Lévy matters III. Lévy-type processes: construction, approximation and sample path properties. Zbl 1384.60004
Böttcher, Björn; Schilling, René; Wang, Jian
2013
A note on the existence of transition probability densities of Lévy processes. Zbl 1269.60050
Knopova, Victoria; Schilling, René L.
2013
Some theorems on Feller processes: transience, local times and ultracontractivity. Zbl 1282.60070
Schilling, René L.; Wang, Jian
2013
Weak order for the discretization of the stochastic heat equation driven by impulsive noise. Zbl 1263.60058
Lindner, Felix; Schilling, René L.
2013
A probabilistic inequality related to negative definite functions. Zbl 1270.60030
Lifshits, Mikhail; Schilling, René L.; Tyurin, Ilya
2013
Stationary distributions for jump processes with inert drift. Zbl 1291.60170
Burdzy, K.; Kulczycki, T.; Schilling, R. L.
2013
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Coupling property and gradient estimates of Lévy processes via the symbol. Zbl 1263.60045
Schilling, René L.; Sztonyk, Paweł; Wang, Jian
2012
Transition density estimates for a class of Lévy and Lévy-type processes. Zbl 1242.60082
Knopova, Viktorya; Schilling, René L.
2012
A geometric interpretation of the transition density of a symmetric Lévy process. Zbl 1279.60097
Jacob, Niels; Knopova, Victorya; Landwehr, Sandra; Schilling, René L.
2012
On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes. Zbl 1247.60113
Schilling, René L.; Wang, Jian
2012
Strong Feller continuity of Feller processes and semigroups. Zbl 1258.60047
Schilling, René L.; Wang, Jian
2012
Functional inequalities and subordination: Stability of Nash and Poincaré inequalities. Zbl 1259.47058
Schilling, René L.; Wang, Jian
2012
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations. Zbl 1273.47070
Butko, Yana A.; Schilling, René L.; Smolyanov, Oleg G.
2012
Brownian motion. An introduction to stochastic processes. With a chapter on simulation by Björn Böttcher. Zbl 1258.60002
Schilling, René L.; Partzsch, Lothar
2012
On the structure of the domain of a symmetric jump-type Dirichlet form. Zbl 1241.31013
Schilling, René L.; Uemura, Toshihiro
2012
Packing dimension profiles and Lévy processes. Zbl 1266.60071
Khoshnevisan, D.; Schilling, R. L.; Xiao, Y.
2012
Adaptive wavelet methods for the stochastic Poisson equation. Zbl 1260.65003
Cioica, Petru A.; Dahlke, Stephan; Döhring, Nicolas; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2012
On the coupling property of Lévy processes. Zbl 1268.60061
Schilling, René L.; Wang, Jian
2011
Constructions of coupling processes for Lévy processes. Zbl 1217.60035
Böttcher, Björn; Schilling, René L.; Wang, Jian
2011
From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class. Zbl 1280.60032
Porcu, Emilio; Schilling, René L.
2011
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Zbl 1250.60026
Cioica, Petru A.; Dahlke, Stephan; Kinzel, Stefan; Lindner, Felix; Raasch, Thorsten; Ritter, Klaus; Schilling, René L.
2011
Feynman formulas and path integrals for some evolution semigroups related to $$\tau$$-quantization. Zbl 1311.58006
Böttcher, B.; Butko, Ya. A.; Schilling, R. L.; Smolyanov, O. G.
2011
Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass. Zbl 1226.81114
Butko, Yana A.; Schilling, Rene L.; Smolyanov, Oleg G.
2011
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
The symbol associated with the solution of a stochastic differential equation. Zbl 1226.60116
Schilling, Rene L.; Schnurr, Alexander
2010
Feynman formulae for Feller semigroups. Zbl 1213.47047
Butko, Ya. A.; Smolyanov, O. G.; Schilling, R. L.
2010
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
Approximation of Feller processes by Markov chains with Lévy increments. Zbl 1168.60359
Böttcher, Björn; Schilling, René L.
2009
On the Feller property of Dirichlet forms generated by pseudo differential operators. Zbl 1141.31006
Schilling, René L.; Uemura, Toshihiro
2007
On a Poincaré-type inequality for energy forms in $$L^p$$. Zbl 1150.31003
Jacob, Niels; Schilling, René L.
2007
Towards an $$L^p$$ potential theory for sub-Markovian semigroups: kernels and capacities. Zbl 1104.31007
Jacob, Niels; Schilling, René L.
2006
Measures, integrals and martingales. Zbl 1084.28001
Schilling, René L.
2005
Function spaces as Dirichlet spaces (about a paper by Maz’ya and Nagel). Zbl 1107.46027
Jacob, Niels; Schilling, René L.
2005
A note on invariant sets. Zbl 1077.47045
Schilling, René L.
2004
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol&rsquo;tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol&rsquo;tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
Lévy-type processes and pseudodifferential operators. Zbl 0984.60054
Jacob, Niels; Schilling, René L.
2001
Function spaces related to continuous negative definite functions: $$\psi$$-Bessel potential spaces. Zbl 0990.46018
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Feller semigroup, $$L^p$$-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. Zbl 0978.47031
Farkas, Walter; Jacob, Niels; Schilling, René L.
2001
Dirichlet operators and the positive maximum principle. Zbl 0994.31003
Schilling, Rene L.
2001
Function spaces as path spaces of Feller processes. Zbl 0970.60043
Schilling, René L.
2000
Sobolev embedding for stochastic processes. Zbl 0970.60044
Schilling, René L.
2000
Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form. Zbl 0970.31008
Jacob, N.; Schilling, R. L.
2000
Some Dirichlet spaces obtained by subordinate reflected diffusions. Zbl 0922.31011
Jacob, Niels; Schilling, René L.
1999
Growth and Hölder conditions for the sample paths of Feller processes. Zbl 0930.60013
Schilling, René L.
1998
Conservativeness and extensions of Feller semigroups. Zbl 0919.47033
Schilling, René L.
1998
Subordination in the sense of Bochner and a related functional calculus. Zbl 0920.47039
Schilling, René L.
1998
Feller processes generated by pseudo-differential operators: On the Hausdorff dimension of their sample paths. Zbl 0910.60028
Schilling, René L.
1998
Conservativeness of semigroups generated by pseudo differential operators. Zbl 0917.60066
Schilling, René L.
1998
An analytic proof of the Lévy-Khinchin formula on $$R^n$$. Zbl 0928.42003
Jacob, Niels; Schilling, René L.
1998
On Feller processes with sample paths in Besov spaces. Zbl 0888.60036
Schilling, René L.
1997
On the domain of the generator of a subordinate semigroup. Zbl 0857.47025
Schilling, René L.
1996
Comparable processes and the Hausdorff dimension of their sample paths. Zbl 0888.60035
Schilling, René L.
1996
Subordination in the sense of S. Bochner – An approach through pseudo differential operators. Zbl 0923.47023
Jacob, Niels; Schilling, René L.
1996
Estimates for Feller semigroups generated by pseudodifferential operators. Zbl 0931.35204
Jacob, Niels; Schilling, René L.
1996
On the path behavior of Markov processes comparable with Lévy processes. (Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy-Prozessen vergleichbar sind.) Zbl 0805.60032
Schilling, René Leander
1994
When does a càdlàg process have continuous sample paths? Zbl 0830.60036
Schilling, René L.
1994
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#### Cited by 755 Authors

 43 Schilling, René Leander 34 Wang, Jian 18 Kim, Panki 14 Chen, Zhen-Qing 14 Kühn, Franziska 13 Grzywny, Tomasz 13 Song, Renming 12 Kaleta, Kamil 12 Vondraček, Zoran 11 Bogdan, Krzysztof 11 Jacob, Niels 11 Kovács, Mihály 11 Qi, Feng 10 Böttcher, Björn 10 Leonenko, Nikolai N. 10 Meerschaert, Mark Marvin 10 Sandrić, Nikola 10 Sztonyk, Paweł 9 Lörinczi, József 8 Kinderknecht, Yana A. 8 Guo, Bai-Ni 8 Knopova, Victoria Pavlovna 8 Uemura, Toshihiro 7 Bäumer, Boris 7 Fageot, Julien 7 Kumagai, Takashi 7 Porcu, Emilio 7 Ryznar, Michał 7 Schnurr, Alexander 7 Smolyanov, Oleg Georgievich 7 Xiao, Yimin 6 Bazhlekova, Emilia G. 6 Deng, Changsong 6 D’Ovidio, Mirko 6 Kassmann, Moritz 6 Kulczycki, Tadeusz 6 Remizov, Ivan D. 6 Röckner, Michael 6 Toaldo, Bruno 6 Wang, Feng-Yu 5 Anh, Vo V. 5 Behme, Anita Diana 5 Dahlke, Stephan 5 Gomilko, Alexandre M. 5 Hanyga, Andrzej 5 Lindner, Felix 5 Mikulevicius, Remigijus 5 Mimica, Ante 5 Nane, Erkan 5 Tomilov, Yuri 5 Unser, Michael A. 5 Vellaisamy, Palaniappan 5 Yang, Xiaochuan 4 Applebaum, David B. 4 Ascione, Giacomo 4 Cygan, Wojciech 4 da Silva, José Luís 4 Evans, Kristian P. 4 Kim, Ildoo 4 Kim, KyeongHun 4 Kondrat’yev, Yuriĭ Grygorovych 4 Kwaśnicki, Mateusz 4 Larsson, Stig 4 Maheshwari, Aditya 4 Mai, Jan-Frederik 4 Menegatto, Valdir Antonio 4 Patie, Pierre 4 Pietruska-Pałuba, Katarzyna 4 Pirozzi, Enrica 4 Ricciuti, Costantino 4 Ruiz-Medina, María Dolores 4 Sakbaev, Vsevolod Zhanovich 4 Shiozawa, Yuichi 4 Sun, Wei 4 Toniazzi, Lorenzo 4 Zhang, Xicheng 4 Zhigljavsky, Anatoly A. 3 Bañuelos, Rodrigo 3 Bazhlekov, Ivan B. 3 Biswas, Anup 3 Chen, Xin 3 Cioica, Petru A. 3 Döhring, Nicolas 3 Fahrenwaldt, Matthias Albrecht 3 Farkas, Walter 3 Hausenblas, Erika 3 Jentzen, Arnulf 3 Jiao, Yong 3 Karp, Dmitriĭ Borisovich 3 Kataria, Kuldeep Kumar 3 Khandakar, Mostafizar 3 Kinzel, Stefan 3 Kobayashi, Kei 3 Kochubeĭ, Anatoliĭ Naumovych 3 Kolokoltsov, Vassili N. 3 Kyprianou, Andreas E. 3 Li, Lingfei 3 Lindner, Alexander M. 3 Ma, Zhi-Ming 3 Magdziarz, Marcin ...and 655 more Authors
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#### Cited in 214 Serials

 43 Stochastic Processes and their Applications 32 Journal of Mathematical Analysis and Applications 31 Journal of Theoretical Probability 27 Potential Analysis 23 Transactions of the American Mathematical Society 21 Bernoulli 20 Journal of Functional Analysis 18 Fractional Calculus & Applied Analysis 16 Statistics & Probability Letters 13 Journal of Differential Equations 12 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 11 Electronic Journal of Probability 10 Journal of Computational and Applied Mathematics 10 Stochastic Analysis and Applications 9 Mathematische Nachrichten 8 Journal of Statistical Physics 8 Proceedings of the American Mathematical Society 7 Probability Theory and Related Fields 7 Journal of Evolution Equations 6 The Annals of Probability 6 Integral Equations and Operator Theory 6 Journal of Applied Probability 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Stochastics and Dynamics 5 Chaos, Solitons and Fractals 5 Acta Mathematica Sinica. English Series 5 ALEA. Latin American Journal of Probability and Mathematical Statistics 5 Science China. Mathematics 5 Stochastic and Partial Differential Equations. Analysis and Computations 4 Advances in Applied Probability 4 Communications in Mathematical Physics 4 Journal d’Analyse Mathématique 4 Studia Mathematica 4 Advances in Mathematics 4 Semigroup Forum 4 Probability and Mathematical Statistics 4 The Annals of Applied Probability 4 Theory of Probability and Mathematical Statistics 4 Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 Mediterranean Journal of Mathematics 3 Computers & Mathematics with Applications 3 Theory of Probability and its Applications 3 Applied Mathematics and Computation 3 BIT 3 Osaka Journal of Mathematics 3 Tohoku Mathematical Journal. Second Series 3 Acta Applicandae Mathematicae 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Russian Journal of Mathematical Physics 3 The Journal of Fourier Analysis and Applications 3 Finance and Stochastics 3 Positivity 3 Communications in Nonlinear Science and Numerical Simulation 3 Communications in Contemporary Mathematics 3 Journal of Physics A: Mathematical and Theoretical 3 Problemy Analiza. Issues of Analysis 3 SIAM/ASA Journal on Uncertainty Quantification 3 Modern Stochastics. Theory and Applications 2 Journal of Mathematical Physics 2 Metrika 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Statistics 2 Automatica 2 Journal of Approximation Theory 2 Journal of Econometrics 2 Journal of the London Mathematical Society. Second Series 2 Journal of Optimization Theory and Applications 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Proceedings of the London Mathematical Society. Third Series 2 Quarterly of Applied Mathematics 2 Zeitschrift für Analysis und ihre Anwendungen 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Constructive Approximation 2 Linear Algebra and its Applications 2 SIAM Journal on Mathematical Analysis 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Statistical Papers 2 Electronic Communications in Probability 2 Doklady Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Vietnam Journal of Mathematics 2 Differential Equations 2 Foundations of Computational Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Communications on Pure and Applied Analysis 2 Banach Journal of Mathematical Analysis 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Analysis and Mathematical Physics 2 Dependence Modeling 1 American Mathematical Monthly 1 Archive for Rational Mechanics and Analysis 1 Indian Journal of Pure & Applied Mathematics 1 International Journal of Theoretical Physics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational Physics 1 Letters in Mathematical Physics ...and 114 more Serials
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#### Cited in 44 Fields

 475 Probability theory and stochastic processes (60-XX) 187 Partial differential equations (35-XX) 141 Operator theory (47-XX) 55 Real functions (26-XX) 54 Potential theory (31-XX) 52 Numerical analysis (65-XX) 44 Functional analysis (46-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 37 Statistics (62-XX) 33 Special functions (33-XX) 28 Integral equations (45-XX) 24 Measure and integration (28-XX) 24 Ordinary differential equations (34-XX) 21 Integral transforms, operational calculus (44-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Statistical mechanics, structure of matter (82-XX) 15 Abstract harmonic analysis (43-XX) 13 Quantum theory (81-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Approximations and expansions (41-XX) 9 Combinatorics (05-XX) 9 Number theory (11-XX) 9 Functions of a complex variable (30-XX) 9 Mechanics of deformable solids (74-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Fluid mechanics (76-XX) 7 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Operations research, mathematical programming (90-XX) 5 Biology and other natural sciences (92-XX) 3 Sequences, series, summability (40-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX)