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Martin Hutzenthaler
Martin Hutzenthaler
Adresse e-mail validée de uni-due.de - Page d'accueil
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Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2011
4862011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
4702012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Society 236 (1112), 2015
2712015
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
M Hutzenthaler, A Jentzen, T Kruse, TA Nguyen
SN partial differential equations and applications 1 (2), 10, 2020
1802020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
M Hutzenthaler, A Jentzen
The Annals of Probability 48 (1), 53-93, 2020
1362020
An overview on deep learning-based approximation methods for partial differential equations
C Beck, M Hutzenthaler, A Jentzen, B Kuckuck
arXiv preprint arXiv:2012.12348, 2020
1342020
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
M Hutzenthaler, A Jentzen, T Kruse, T Anh Nguyen, P von Wurstemberger
Proceedings of the Royal Society A 476 (2244), 20190630, 2020
1232020
Loss of regularity for Kolmogorov equations
M Hairer, M Hutzenthaler, A Jentzen
1162015
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
M Hutzenthaler, A Jentzen, PE Kloeden
1042013
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic …
W E, M Hutzenthaler, A Jentzen, T Kruse
Journal of Scientific Computing 79 (3), 1534-1571, 2019
79*2019
Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
S Cox, M Hutzenthaler, A Jentzen
arXiv preprint arXiv:1309.5595, 2013
762013
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
W E, M Hutzenthaler, A Jentzen, T Kruse
Partial Differential Equations and Applications 2 (6), 1-31, 2021
70*2021
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
M Hutzenthaler, A Jentzen, X Wang
Mathematics of Computation 87 (311), 1353-1413, 2018
702018
Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
M Hutzenthaler, T Kruse
SIAM Journal on Numerical Analysis 58 (2), 929-961, 2020
582020
Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard …
C Beck, F Hornung, M Hutzenthaler, A Jentzen, T Kruse
Journal of Numerical Mathematics 28 (4), 197-222, 2020
572020
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
M Hutzenthaler, A Jentzen, W Wurstemberger
542020
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
M Hutzenthaler, A Jentzen, T Kruse
Foundations of Computational Mathematics 22 (4), 905-966, 2022
492022
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
M Hutzenthaler, A Jentzen
Foundations of Computational Mathematics, 1-50, 2011
482011
Ergodic behavior of locally regulated branching populations
M Hutzenthaler, A Wakolbinger
472007
Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries
M Hutzenthaler, A Jentzen, M Noll
arXiv preprint arXiv:1403.6385, 2014
402014
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