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Martin Hutzenthaler
Martin Hutzenthaler
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Zitiert von
Zitiert von
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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
3782011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
The Annals of Applied Probability 22 (4), 1611-1641, 2012
3722012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Soc., 2015
2332015
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), 1-34, 2020
1232020
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
1082020
Loss of regularity for Kolmogorov equations
M Hairer, M Hutzenthaler, A Jentzen
The Annals of Probability 43 (2), 468-527, 2015
962015
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
M Hutzenthaler, A Jentzen, PE Kloeden
The Annals of Applied Probability 23 (5), 1913-1966, 2013
932013
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
822020
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
632013
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
552018
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
49*2019
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
45*2021
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
432020
Ergodic behavior of locally regulated branching populations
M Hutzenthaler, A Wakolbinger
The Annals of Applied Probability 17 (2), 474-501, 2007
432007
Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
M Hutzenthaler, A Jentzen
Foundations of Computational Mathematics, 1-50, 2011
422011
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
412020
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
392020
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
M Hutzenthaler, A Jentzen
Electronic Journal of Probability 25, 1-73, 2020
362020
Norovirus GII. 4 and GII. 7 capsid sequences undergo positive selection in chronically infected patients
D Hoffmann, M Hutzenthaler, J Seebach, M Panning, A Umgelter, ...
Infection, Genetics and Evolution 12 (2), 461-466, 2012
362012
Branching diffusions in random environment
C Boeinghoff, M Hutzenthaler
arXiv preprint arXiv:1107.2773, 2011
362011
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