## Jentzen, Arnulf

Compute Distance To:
 Author ID: jentzen.arnulf Published as: Jentzen, Arnulf; Jentzen, A. Homepage: http://www.ajentzen.de/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND Awards: Felix Klein Prize (2020)
 Documents Indexed: 77 Publications since 2007, including 2 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 54 Co-Authors with 76 Joint Publications 1,294 Co-Co-Authors
all top 5

### Co-Authors

 3 single-authored 19 Hutzenthaler, Martin 15 Kloeden, Peter Eris 8 Becker, Sebastian 7 Beck, Christian 7 E, Weinan 7 Welti, Timo 6 Kurniawan, Ryan 6 Pušnik, Primož 5 Cheridito, Patrick 5 Kruse, Thomas 5 von Wurstemberger, Philippe 4 Salimova, Diyora F. 3 Andersson, Adam 3 Grohs, Philipp 3 Han, Jiequn 3 Kuckuck, Benno 3 Lindner, Felix 3 Neuenkirch, Andreas 3 Röckner, Michael 2 Cox, Sonja Gisela 2 Gess, Benjamin 2 Hefter, Mario 2 Jacobe de Naurois, Ladislas 2 Müller-Gronbach, Thomas 2 Neufeld, Ariel David 2 Nguyen, Tuan-Anh 2 Rossmannek, Florian 2 Yaroslavtseva, Larisa 1 Berger, Arno 1 Berner, Julius 1 Blömker, Dirk 1 Braunwarth, Ramon 1 Caraballo Garrido, Tomás 1 Conus, Daniel 1 Da Prato, Giuseppe 1 Elbrächter, Dennis 1 Fehrman, Benjamin J. 1 Gerencsér, Máté 1 Gonon, Lukas 1 Hairer, Martin 1 Han, Xiaoying 1 Hornung, Fabian 1 Jaafari, Nor 1 Leber, Frank 1 Riekert, Adrian 1 Schneisgen, Daniela 1 Schwab, Christoph 1 Shen, Hao 1 Siegmund, Stefan 1 Stadtmüller, Uli 1 Stelzer, Robert 1 van Neerven, Jan M. A. M. 1 Wang, Xiaojie 1 Winkel, Georg
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### Serials

 5 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Mathematical Analysis and Applications 4 The Annals of Applied Probability 3 IMA Journal of Numerical Analysis 3 The Annals of Probability 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 SIAM Journal on Numerical Analysis 3 Journal of Complexity 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Foundations of Computational Mathematics 3 Communications in Mathematical Sciences 2 BIT 2 Journal of Scientific Computing 2 Potential Analysis 2 Journal of Machine Learning Research (JMLR) 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 SN Partial Differential Equations and Applications 1 Bulletin of the Australian Mathematical Society 1 Nonlinearity 1 Mathematics of Computation 1 Applied Mathematics and Optimization 1 IEEE Transactions on Automatic Control 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Transactions of the American Mathematical Society 1 Constructive Approximation 1 European Journal of Applied Mathematics 1 Numerical Algorithms 1 Proceedings of the National Academy of Sciences of the United States of America 1 Stochastic Processes and their Applications 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Electronic Journal of Probability 1 Finance and Stochastics 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Journal of Numerical Mathematics 1 Stochastics and Dynamics 1 Milan Journal of Mathematics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Communications in Computational Physics 1 Communications in Mathematics and Statistics 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 SIAM Journal on Mathematics of Data Science
all top 5

### Fields

 54 Probability theory and stochastic processes (60-XX) 53 Numerical analysis (65-XX) 32 Partial differential equations (35-XX) 13 Ordinary differential equations (34-XX) 12 Computer science (68-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Approximations and expansions (41-XX) 3 Statistics (62-XX) 2 General and overarching topics; collections (00-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

69 Publications have been cited 1,666 times in 831 Documents Cited by Year
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
2018
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2012
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
2017
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084
Hutzenthaler, Martin; Jentzen, Arnulf
2015
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011
Jentzen, Arnulf; Kloeden, Peter E.
2009
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
2011
The numerical approximation of stochastic partial differential equations. Zbl 1205.60130
Jentzen, A.; Kloeden, P. E.
2009
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
2019
Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071
Blömker, Dirk; Jentzen, Arnulf
2013
Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2009
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030
Jentzen, Arnulf; Röckner, Michael
2012
Deep optimal stopping. Zbl 07064054
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf
2019
Loss of regularity for Kolmogorov equations. Zbl 1322.35083
Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
2015
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051
Jentzen, Arnulf
2009
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
2011
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2013
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2019
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
2010
A Milstein scheme for SPDEs. Zbl 1318.60072
Jentzen, Arnulf; Röckner, Michael
2015
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
2020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753
Hutzenthaler, Martin; Jentzen, Arnulf
2020
Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052
Becker, Sebastian; Jentzen, Arnulf
2019
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006
Hutzenthaler, Martin; Jentzen, Arnulf
2011
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011
Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie
2018
A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003
Jentzen, A.; Neuenkirch, A.
2009
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020
Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
2019
On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012
Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
2016
Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015
Kloeden, Peter E.; Jentzen, Arnulf
2007
Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305
Jentzen, Arnulf; Kloeden, Peter E.
2009
Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015
Jentzen, Arnulf
2011
A mild Itô formula for SPDEs. Zbl 1423.35472
Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael
2019
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220
Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161
Jentzen, Arnulf; Pušnik, Primož
2020
Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 1480.60191
Berner, Julius; Grohs, Philipp; Jentzen, Arnulf
2020
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. Zbl 1471.65169
Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2020
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe
2020
Solving the Kolmogorov PDE by means of deep learning. Zbl 07389370
Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf
2021
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102
Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora
2019
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
2016
An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068
Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E.
2016
Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064
Jentzen, Arnulf
2010
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
2019
Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. Zbl 1475.65157
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
2021
On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo
2017
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
2017
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401
Hefter, Mario; Jentzen, Arnulf
2019
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
2018
Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072
Jentzen, Arnulf; Pušnik, Primož
2018
Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353
Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071
Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe
2021
Deep splitting method for parabolic PDEs. Zbl 07395807
Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel
2021
Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 07255167
Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf
2020
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051
Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan
2019
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054
Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo
2021
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251
Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Solving high-dimensional optimal stopping problems using deep learning. Zbl 07441301
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo
2021
Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 07361982
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
2021
An improved maximum allowable transfer interval for $$L^p$$-stability of networked control systems. Zbl 1368.93642
Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan
2010
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143
Jentzen, Arnulf; Kurniawan, Ryan
2021
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670
2021
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2021
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 07455604
E, Weinan; Han, Jiequn; Jentzen, Arnulf
2022
Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2009
On the mild Itô formula in Banach spaces. Zbl 1402.60067
Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož
2018
On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096
Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf
2021
DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 07493716
Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph
2022
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
2020
A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051
Jentzen, A.; Kloeden, P. E.
2010
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 07455604
E, Weinan; Han, Jiequn; Jentzen, Arnulf
2022
DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 07493716
Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph
2022
Solving the Kolmogorov PDE by means of deep learning. Zbl 07389370
Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf
2021
Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. Zbl 1475.65157
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
2021
Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071
Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe
2021
Deep splitting method for parabolic PDEs. Zbl 07395807
Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel
2021
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054
Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo
2021
Solving high-dimensional optimal stopping problems using deep learning. Zbl 07441301
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo
2021
Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 07361982
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian
2021
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143
Jentzen, Arnulf; Kurniawan, Ryan
2021
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670
2021
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2021
On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096
Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf
2021
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
2020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753
Hutzenthaler, Martin; Jentzen, Arnulf
2020
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220
Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161
Jentzen, Arnulf; Pušnik, Primož
2020
Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Zbl 1480.60191
Berner, Julius; Grohs, Philipp; Jentzen, Arnulf
2020
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. Zbl 1471.65169
Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2020
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe
2020
Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353
Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 07255167
Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf
2020
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251
Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
2020
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111
Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E.
2020
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
2019
Deep optimal stopping. Zbl 07064054
Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf
2019
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2019
Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052
Becker, Sebastian; Jentzen, Arnulf
2019
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020
Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
2019
A mild Itô formula for SPDEs. Zbl 1423.35472
Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael
2019
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102
Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora
2019
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo
2019
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401
Hefter, Mario; Jentzen, Arnulf
2019
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051
Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan
2019
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
2018
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011
Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie
2018
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094
Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo
2018
Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072
Jentzen, Arnulf; Pušnik, Primož
2018
On the mild Itô formula in Banach spaces. Zbl 1402.60067
Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož
2018
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
2017
On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092
Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo
2017
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
2017
On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012
Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa
2016
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
2016
An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068
Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E.
2016
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084
Hutzenthaler, Martin; Jentzen, Arnulf
2015
Loss of regularity for Kolmogorov equations. Zbl 1322.35083
Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
2015
A Milstein scheme for SPDEs. Zbl 1318.60072
Jentzen, Arnulf; Röckner, Michael
2015
Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071
Blömker, Dirk; Jentzen, Arnulf
2013
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2013
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2012
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030
Jentzen, Arnulf; Röckner, Michael
2012
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
2011
Taylor approximations for stochastic partial differential equations. Zbl 1240.35001
Jentzen, Arnulf; Kloeden, Peter
2011
Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
2011
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006
Hutzenthaler, Martin; Jentzen, Arnulf
2011
Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015
Jentzen, Arnulf
2011
Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202
Jentzen, Arnulf; Kloeden, Peter
2010
Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064
Jentzen, Arnulf
2010
An improved maximum allowable transfer interval for $$L^p$$-stability of networked control systems. Zbl 1368.93642
Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan
2010
A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051
Jentzen, A.; Kloeden, P. E.
2010
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011
Jentzen, Arnulf; Kloeden, Peter E.
2009
The numerical approximation of stochastic partial differential equations. Zbl 1205.60130
Jentzen, A.; Kloeden, P. E.
2009
Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2009
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051
Jentzen, Arnulf
2009
A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003
Jentzen, A.; Neuenkirch, A.
2009
Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305
Jentzen, Arnulf; Kloeden, Peter E.
2009
Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009
Jentzen, A.; Kloeden, P. E.; Neuenkirch, A.
2009
Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015
Kloeden, Peter E.; Jentzen, Arnulf
2007
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### Cited by 1,192 Authors

 51 Jentzen, Arnulf 22 Kloeden, Peter Eris 21 Hutzenthaler, Martin 21 Wang, Xiaojie 19 Mao, Xuerong 12 Gan, Siqing 11 E, Weinan 11 Hong, Jialin 11 Tambue, Antoine 10 Karniadakis, George Em 10 Liu, Wei 10 Szpruch, Lukasz 9 Kruse, Raphael 9 Kruse, Thomas 9 Ngo, Hoang-Long 9 Przybyłowicz, Paweł 9 Redmann, Martin 9 Reisinger, Christoph 8 Cui, Jianbo 8 Kovács, Mihály 8 Kumar, Chaman 8 Lang, Annika 8 Larsson, Stig 8 Lord, Gabriel James 8 Neuenkirch, Andreas 8 Sabanis, Sotirios 8 Schwab, Christoph 7 Andersson, Adam 7 Beck, Christian 7 Becker, Sebastian 7 Han, Jiequn 7 Kamrani, Minoo 7 Warin, Xavier 7 Yuan, Chenggui 6 Blömker, Dirk 6 Hu, Junhao 6 Kuznetsov, Dmitriĭ Feliksovich 6 Li, Xiaoyue 6 Liu, Mingzhu 6 Mishra, Siddhartha 6 Mukam, Jean Daniel 6 Petersen, Philipp Christian 6 Qi, Ruisheng 6 Song, Minghui 6 Taguchi, Dai 6 Ying, Lexing 6 Zhao, Weidong 5 Bachouch, Achref 5 Bréhier, Charles-Edouard 5 Cao, Yanzhao 5 Duan, Jinqiao 5 Grohs, Philipp 5 Huang, Chengming 5 Kühn, Christian 5 Kurniawan, Ryan 5 Lindner, Felix 5 Liu, Zhihui 5 Lu, Jianfeng 5 Müller-Gronbach, Thomas 5 Pham, Huyên 5 Schneider, Reinhold 5 Tan, Li 5 Yang, Hongfu 5 Yang, Xu 5 Yaroslavtseva, Larisa 5 Yin, George Gang 4 Asai, Yusuke 4 Bao, Feng 4 Bayer, Christian 4 Deya, Aurélien 4 dos Reis, Gonçalo 4 Gao, Shuaibin 4 Giles, Michael B. 4 Guo, Qian 4 Hairer, Martin 4 Halidias, Nikolaos 4 Han, Xiaoying 4 Hefter, Mario 4 Jerez, Silvia 4 Kutyniok, Gitta 4 Luong, Duc-Trong 4 Matoussi, Anis 4 Milošević, Marija 4 Mirzaee, Farshid 4 Morkisz, Paweł M. 4 Nguyen, Tuan-Anh 4 Oh, Tadahiro 4 Perdikaris, Paris G. 4 Raslan, Mones 4 Rößler, Andreas 4 Šiška, David 4 Stannat, Wilhelm 4 Szölgyenyi, Michaela 4 Welti, Timo 4 Wu, Fuke 4 Wu, Yue 4 Yang, Huizi 4 Yi, Yulian 4 Zhang, Qimin 4 Zhao, Jingjun ...and 1,092 more Authors
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### Cited in 192 Serials

 61 Journal of Computational and Applied Mathematics 51 Journal of Computational Physics 37 Applied Mathematics and Computation 26 SIAM Journal on Numerical Analysis 23 Journal of Scientific Computing 22 Communications in Computational Physics 21 Computer Methods in Applied Mechanics and Engineering 21 Journal of Mathematical Analysis and Applications 21 Applied Numerical Mathematics 18 Stochastic and Partial Differential Equations. Analysis and Computations 17 BIT 16 International Journal of Computer Mathematics 16 SIAM Journal on Scientific Computing 15 The Annals of Applied Probability 14 Stochastic Processes and their Applications 13 Numerical Algorithms 12 Mathematics of Computation 12 Discrete and Continuous Dynamical Systems. Series B 10 Stochastic Analysis and Applications 10 SIAM Journal on Financial Mathematics 9 Journal of Differential Equations 9 Monte Carlo Methods and Applications 9 Quantitative Finance 8 Numerische Mathematik 7 Journal of Complexity 7 Multiscale Modeling & Simulation 7 Advances in Difference Equations 6 Electronic Journal of Probability 6 Differentsial’nye Uravneniya i Protsessy Upravleniya 6 Foundations of Computational Mathematics 6 Stochastics and Dynamics 5 Computers & Mathematics with Applications 5 Applied Mathematics and Optimization 5 Calcolo 5 Mathematics and Computers in Simulation 5 Physica D 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Abstract and Applied Analysis 5 Analysis and Applications (Singapore) 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Research in the Mathematical Sciences 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Statistics & Probability Letters 4 Constructive Approximation 4 European Journal of Applied Mathematics 4 Finance and Stochastics 4 Communications in Nonlinear Science and Numerical Simulation 4 SN Partial Differential Equations and Applications 4 SIAM Journal on Mathematics of Data Science 3 Journal of the Franklin Institute 3 Journal of Statistical Physics 3 Mathematical Methods in the Applied Sciences 3 Nonlinearity 3 Chaos, Solitons and Fractals 3 The Annals of Probability 3 Memoirs of the American Mathematical Society 3 SIAM Journal on Control and Optimization 3 Systems & Control Letters 3 Computational Mechanics 3 Potential Analysis 3 Computational and Applied Mathematics 3 Advances in Computational Mathematics 3 Engineering Analysis with Boundary Elements 3 Discrete and Continuous Dynamical Systems 3 Nonlinear Dynamics 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Journal of Applied Mathematics and Computing 3 Discrete and Continuous Dynamical Systems. Series S 3 Statistics and Computing 3 SIAM/ASA Journal on Uncertainty Quantification 3 Journal of Mathematical Modeling 2 Computers and Fluids 2 Communications in Mathematical Physics 2 Physics Letters. A 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Inventiones Mathematicae 2 Transactions of the American Mathematical Society 2 Insurance Mathematics & Economics 2 Chinese Annals of Mathematics. Series B 2 Journal of Computational Mathematics 2 Journal of Theoretical Probability 2 Applied Mathematics Letters 2 MCSS. Mathematics of Control, Signals, and Systems 2 Communications in Statistics. Theory and Methods 2 SIAM Review 2 Journal of Nonlinear Science 2 Journal of Difference Equations and Applications 2 Electronic Communications in Probability 2 Bernoulli 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Vietnam Journal of Mathematics 2 Chaos 2 Discrete Dynamics in Nature and Society 2 International Journal of Theoretical and Applied Finance 2 Methodology and Computing in Applied Probability 2 Journal of Evolution Equations 2 Journal of Numerical Mathematics 2 Oberwolfach Reports 2 Stochastics ...and 92 more Serials
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### Cited in 40 Fields

 575 Numerical analysis (65-XX) 532 Probability theory and stochastic processes (60-XX) 208 Partial differential equations (35-XX) 145 Computer science (68-XX) 90 Ordinary differential equations (34-XX) 66 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Systems theory; control (93-XX) 47 Biology and other natural sciences (92-XX) 41 Statistics (62-XX) 36 Dynamical systems and ergodic theory (37-XX) 33 Fluid mechanics (76-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 24 Approximations and expansions (41-XX) 21 Statistical mechanics, structure of matter (82-XX) 21 Operations research, mathematical programming (90-XX) 15 Integral equations (45-XX) 12 Operator theory (47-XX) 12 Mechanics of deformable solids (74-XX) 11 Functional analysis (46-XX) 11 Quantum theory (81-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Optics, electromagnetic theory (78-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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