Arnulf Jentzen

Overview

Best Publications

• Solving high-dimensional partial differential equations using deep learning

  Jiequn Han;Arnulf Jentzen;Weinan E

  1751
  Citations

• Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

  Weinan E;Weinan E;Jiequn Han;Arnulf Jentzen

  846
  Citations

• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

  Martin Hutzenthaler;Arnulf Jentzen;Peter E. Kloeden

  496
  Citations

• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

  Martin Hutzenthaler;Arnulf Jentzen;Peter E. Kloeden

  481
  Citations

• Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

  Christian Beck;Weinan E;Arnulf Jentzen

  325
  Citations

• Numerical Approximations of Stochastic Differential Equations With Non-globally Lipschitz Continuous Coefficients

  Martin Hutzenthaler;Arnulf Jentzen

  273
  Citations

• A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

  Philipp Grohs;Fabian Hornung;Arnulf Jentzen;Philippe von Wurstemberger

  235
  Citations

• 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

  Julius Berner;Philipp Grohs;Arnulf Jentzen

  234
  Citations

• A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

  Martin Hutzenthaler;Arnulf Jentzen;Arnulf Jentzen;Thomas Kruse;Tuan Anh Nguyen

  221
  Citations

• The Numerical Approximation of Stochastic Partial Differential Equations

  A. Jentzen;P. E. Kloeden

  197
  Citations

• Taylor Approximations for Stochastic Partial Differential Equations

  Arnulf Jentzen;Peter E. Kloeden

  189
  Citations

• Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise

  Arnulf Jentzen;Peter E Kloeden

  185
  Citations

• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients

  Martin Hutzenthaler;Arnulf Jentzen

  165
  Citations

• Deep Splitting Method for Parabolic PDEs

  Christian Beck;Sebastian Becker;Patrick Cheridito;Arnulf Jentzen

  155
  Citations

• Solving stochastic differential equations and Kolmogorov equations by means of deep learning.

  Christian Beck;Sebastian Becker;Philipp Grohs;Nor Jaafari

  153
  Citations

• Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning.

  Weinan E;Jiequn Han;Arnulf Jentzen

  147
  Citations

• A 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

  Arnulf Jentzen;Diyora Salimova;Timo Welti

  143
  Citations

• DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

  Dennis Elbrächter;Philipp Grohs;Philipp Grohs;Arnulf Jentzen;Arnulf Jentzen;Christoph Schwab

  128
  Citations

• Deep Optimal Stopping

  Sebastian Becker;Patrick Cheridito;Arnulf Jentzen

  127
  Citations

• Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise

  Arnulf Jentzen;Michael Röckner;Michael Röckner

  121
  Citations

• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

  Weinan E;Martin Hutzenthaler;Arnulf Jentzen;Thomas Kruse

  108
  Citations

• On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

  Weinan E;Martin Hutzenthaler;Arnulf Jentzen;Thomas Kruse

  104
  Citations

• Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz

  Arnulf Jentzen;Peter E. Kloeden

  0
  Citations