Edit Profile (opens in new tab) Jentzen, Arnulf Compute Distance To: Compute 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1416.35137Han, Jiequn; Jentzen, Arnulf; E, Weinan 168 2018 Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 168 2011 Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 144 2012 Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016E, Weinan; Han, Jiequn; Jentzen, Arnulf 125 2017 Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084Hutzenthaler, Martin; Jentzen, Arnulf 74 2015 Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011Jentzen, Arnulf; Kloeden, Peter E. 68 2009 Taylor approximations for stochastic partial differential equations. Zbl 1240.35001Jentzen, Arnulf; Kloeden, Peter 54 2011 The numerical approximation of stochastic partial differential equations. Zbl 1205.60130Jentzen, A.; Kloeden, P. E. 52 2009 Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116Beck, Christian; E, Weinan; Jentzen, Arnulf 51 2019 Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071Blömker, Dirk; Jentzen, Arnulf 38 2013 Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003Jentzen, A.; Kloeden, P. E.; Neuenkirch, A. 37 2009 Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030Jentzen, Arnulf; Röckner, Michael 37 2012 Deep optimal stopping. Zbl 07064054Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf 35 2019 Loss of regularity for Kolmogorov equations. Zbl 1322.35083Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf 34 2015 Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051Jentzen, Arnulf 33 2009 Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg 32 2011 Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 32 2013 On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 29 2019 Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202Jentzen, Arnulf; Kloeden, Peter 27 2010 A Milstein scheme for SPDEs. Zbl 1318.60072Jentzen, Arnulf; Röckner, Michael 24 2015 A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh 21 2020 On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753Hutzenthaler, Martin; Jentzen, Arnulf 21 2020 Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052Becker, Sebastian; Jentzen, Arnulf 19 2019 Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006Hutzenthaler, Martin; Jentzen, Arnulf 19 2011 Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie 18 2018 A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003Jentzen, A.; Neuenkirch, A. 18 2009 Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan 17 2019 On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa 17 2016 Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015Kloeden, Peter E.; Jentzen, Arnulf 16 2007 Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305Jentzen, Arnulf; Kloeden, Peter E. 13 2009 Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015Jentzen, Arnulf 13 2011 A mild Itô formula for SPDEs. Zbl 1423.35472Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael 13 2019 Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe 12 2020 Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161Jentzen, Arnulf; Pušnik, Primož 11 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 1480.60191Berner, Julius; Grohs, Philipp; Jentzen, Arnulf 11 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 1471.65169Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 10 2020 Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe 10 2020 Solving the Kolmogorov PDE by means of deep learning. Zbl 07389370Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf 10 2021 Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora 10 2019 Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094E, Weinan; Jentzen, Arnulf; Shen, Hao 10 2016 An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E. 10 2016 Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064Jentzen, Arnulf 9 2010 Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059Jentzen, Arnulf; Salimova, Diyora; Welti, Timo 8 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 1475.65157Jentzen, Arnulf; Salimova, Diyora; Welti, Timo 7 2021 On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo 6 2017 On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora 5 2017 On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401Hefter, Mario; Jentzen, Arnulf 5 2019 Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo 5 2018 Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072Jentzen, Arnulf; Pušnik, Primož 5 2018 Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353Jentzen, Arnulf; von Wurstemberger, Philippe 5 2020 Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe 4 2021 Deep splitting method for parabolic PDEs. Zbl 07395807Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel 4 2021 Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 07255167Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf 4 2020 Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan 4 2019 Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo 3 2021 Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe 3 2020 Solving high-dimensional optimal stopping problems using deep learning. Zbl 07441301Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo 3 2021 Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 07361982Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian 3 2021 An improved maximum allowable transfer interval for \(L^p\)-stability of networked control systems. Zbl 1368.93642Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan 3 2010 Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143Jentzen, Arnulf; Kurniawan, Ryan 3 2021 Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan 2 2021 Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 2 2021 Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 07455604E, Weinan; Han, Jiequn; Jentzen, Arnulf 2 2022 Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009Jentzen, A.; Kloeden, P. E.; Neuenkirch, A. 2 2009 On the mild Itô formula in Banach spaces. Zbl 1402.60067Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož 2 2018 On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf 2 2021 DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 07493716Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph 2 2022 Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E. 1 2020 A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051Jentzen, A.; Kloeden, P. E. 1 2010 Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. Zbl 07455604E, Weinan; Han, Jiequn; Jentzen, Arnulf 2 2022 DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 07493716Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph 2 2022 Solving the Kolmogorov PDE by means of deep learning. Zbl 07389370Beck, Christian; Becker, Sebastian; Grohs, Philipp; Jaafari, Nor; Jentzen, Arnulf 10 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 1475.65157Jentzen, Arnulf; Salimova, Diyora; Welti, Timo 7 2021 Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe 4 2021 Deep splitting method for parabolic PDEs. Zbl 07395807Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel 4 2021 Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo 3 2021 Solving high-dimensional optimal stopping problems using deep learning. Zbl 07441301Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Welti, Timo 3 2021 Non-convergence of stochastic gradient descent in the training of deep neural networks. Zbl 07361982Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian 3 2021 Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143Jentzen, Arnulf; Kurniawan, Ryan 3 2021 Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Zbl 1473.35670Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan 2 2021 Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. Zbl 1476.65273E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 2 2021 On existence and uniqueness properties for solutions of stochastic fixed point equations. Zbl 1462.60096Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf 2 2021 A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. Zbl 1455.65200Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh 21 2020 On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Zbl 07206753Hutzenthaler, Martin; Jentzen, Arnulf 21 2020 Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Zbl 1469.60220Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe 12 2020 Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161Jentzen, Arnulf; Pušnik, Primož 11 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 1480.60191Berner, Julius; Grohs, Philipp; Jentzen, Arnulf 11 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 1471.65169Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 10 2020 Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Zbl 1472.65157Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh; von Wurstemberger, Philippe 10 2020 Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. Zbl 1433.68353Jentzen, Arnulf; von Wurstemberger, Philippe 5 2020 Convergence rates for the stochastic gradient descent method for non-convex objective functions. Zbl 07255167Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf 4 2020 Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Zbl 1473.65251Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe 3 2020 Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Zbl 1472.60111Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; Kloeden, Peter E. 1 2020 Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116Beck, Christian; E, Weinan; Jentzen, Arnulf 51 2019 Deep optimal stopping. Zbl 07064054Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf 35 2019 On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas 29 2019 Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. Zbl 1403.60052Becker, Sebastian; Jentzen, Arnulf 19 2019 Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. Zbl 1477.65020Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan 17 2019 A mild Itô formula for SPDEs. Zbl 1423.35472Da Prato, Giuseppe; Jentzen, Arnulf; Röckner, Michael 13 2019 Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Zbl 1406.60102Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora 10 2019 Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. Zbl 1403.60059Jentzen, Arnulf; Salimova, Diyora; Welti, Timo 8 2019 On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Zbl 1425.91401Hefter, Mario; Jentzen, Arnulf 5 2019 Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces. Zbl 1431.60051Andersson, Adam; Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan 4 2019 Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137Han, Jiequn; Jentzen, Arnulf; E, Weinan 168 2018 Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Zbl 1432.65011Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie 18 2018 Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations. Zbl 1405.60094Jacobe de Naurois, Ladislas; Jentzen, Arnulf; Welti, Timo 5 2018 Exponential moments for numerical approximations of stochastic partial differential equations. Zbl 1416.60072Jentzen, Arnulf; Pušnik, Primož 5 2018 On the mild Itô formula in Banach spaces. Zbl 1402.60067Cox, Sonja; Jentzen, Arnulf; Kurniawan, Ryan; Pušnik, Primož 2 2018 Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016E, Weinan; Han, Jiequn; Jentzen, Arnulf 125 2017 On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Zbl 1373.34092Andersson, Adam; Jentzen, Arnulf; Kurniawan, Ryan; Welti, Timo 6 2017 On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Zbl 1404.60082Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora 5 2017 On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Zbl 1355.65012Jentzen, Arnulf; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa 17 2016 Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094E, Weinan; Jentzen, Arnulf; Shen, Hao 10 2016 An exponential Wagner-Platen type scheme for SPDEs. Zbl 1345.60068Becker, Sebastian; Jentzen, Arnulf; Kloeden, Peter E. 10 2016 Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1330.60084Hutzenthaler, Martin; Jentzen, Arnulf 74 2015 Loss of regularity for Kolmogorov equations. Zbl 1322.35083Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf 34 2015 A Milstein scheme for SPDEs. Zbl 1318.60072Jentzen, Arnulf; Röckner, Michael 24 2015 Galerkin approximations for the stochastic Burgers equation. Zbl 1267.60071Blömker, Dirk; Jentzen, Arnulf 38 2013 Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations. Zbl 1283.60098Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 32 2013 Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Zbl 1256.65003Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 144 2012 Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Zbl 1241.60030Jentzen, Arnulf; Röckner, Michael 37 2012 Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Zbl 1228.65014Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. 168 2011 Taylor approximations for stochastic partial differential equations. Zbl 1240.35001Jentzen, Arnulf; Kloeden, Peter 54 2011 Efficient simulation of nonlinear parabolic SPDEs with additive noise. Zbl 1223.60050Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg 32 2011 Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Zbl 1253.65006Hutzenthaler, Martin; Jentzen, Arnulf 19 2011 Higher order pathwise numerical approximations of SPDEs with additive noise. Zbl 1228.65015Jentzen, Arnulf 13 2011 Taylor expansions of solutions of stochastic partial differential equations with additive noise. Zbl 1220.35202Jentzen, Arnulf; Kloeden, Peter 27 2010 Taylor expansions of solutions of stochastic partial differential equations. Zbl 1201.60064Jentzen, Arnulf 9 2010 An improved maximum allowable transfer interval for \(L^p\)-stability of networked control systems. Zbl 1368.93642Jentzen, Arnulf; Leber, Frank; Schneisgen, Daniela; Berger, Arno; Siegmund, Stefan 3 2010 A unified existence and uniqueness theorem for stochastic evolution equations. Zbl 1200.60051Jentzen, A.; Kloeden, P. E. 1 2010 Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Zbl 1186.65011Jentzen, Arnulf; Kloeden, Peter E. 68 2009 The numerical approximation of stochastic partial differential equations. Zbl 1205.60130Jentzen, A.; Kloeden, P. E. 52 2009 Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients. Zbl 1163.65003Jentzen, A.; Kloeden, P. E.; Neuenkirch, A. 37 2009 Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Zbl 1176.60051Jentzen, Arnulf 33 2009 A random Euler scheme for Carathéodory differential equations. Zbl 1160.65003Jentzen, A.; Neuenkirch, A. 18 2009 Pathwise Taylor schemes for random ordinary differential equations. Zbl 1162.65305Jentzen, Arnulf; Kloeden, Peter E. 13 2009 Pathwise convergence of numerical schemes for random and stochastic differential equations. Zbl 1179.65009Jentzen, A.; Kloeden, P. E.; Neuenkirch, A. 2 2009 Pathwise convergent higher order numerical schemes for random ordinary differential equations. Zbl 1140.65015Kloeden, Peter E.; Jentzen, Arnulf 16 2007 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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