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1

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations

Hutzenthaler, Martin, Jentzen, Arnulf, Kloeden, Peter E.

Journal:

The Annals of Applied Probability

Year:

2013

Language:

english

File:

PDF, 594 KB

english, 2013

2

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

Hutzenthaler, M., Jentzen, A., Kloeden, P. E.

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2011

Language:

english

File:

PDF, 210 KB

english, 2011

3

Loss of regularity for Kolmogorov equations

Hairer, Martin, Hutzenthaler, Martin, Jentzen, Arnulf

Journal:

The Annals of Probability

Year:

2015

Language:

english

File:

PDF, 584 KB

english, 2015

4

Time reversal of some stationary jump diffusion processes from population genetics

Hutzenthaler, Martin, Taylor, Jesse Earl

Journal:

Advances in Applied Probability

Year:

2010

Language:

english

File:

PDF, 286 KB

english, 2010

5

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations

Hutzenthaler, Martin, Jentzen, Arnulf, Wang, Xiaojie

Journal:

Mathematics of Computation

Year:

2017

Language:

english

File:

PDF, 733 KB

english, 2017

6

Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

Martin Hutzenthaler, Arnulf Jentzen

Journal:

Foundations of Computational Mathematics

Year:

2011

Language:

english

File:

PDF, 1.34 MB

english, 2011

7

Norovirus GII.4 and GII.7 capsid sequences undergo positive selection in chronically infected patients

Dieter Hoffmann, Martin Hutzenthaler, Judith Seebach, Marcus Panning, Andreas Umgelter, Helge Menzel, Ulrike Protzer, Dirk Metzler

Journal:

Infection, Genetics and Evolution

Year:

2012

Language:

english

File:

PDF, 432 KB

english, 2012

8

Ecological and genetic effects of introduced species on their native competitors

Wittmann, Meike J., Hutzenthaler, Martin, Gabriel, Wilfried, Metzler, Dirk

Journal:

Theoretical Population Biology

Year:

2013

Language:

english

File:

PDF, 795 KB

english, 2013

9

TIME REVERSAL OF SOME STATIONARY JUMP DIFFUSION PROCESSES FROM POPULATION GENETICS

MARTIN HUTZENTHALER and JESSE EARL TAYLOR

Journal:

Advances in Applied Probability

Year:

2010

Language:

english

File:

PDF, 1.78 MB

english, 2010

10

Ergodic Behavior of Locally Regulated Branching Populations

M. Hutzenthaler and A. Wakolbinger

Journal:

The Annals of Applied Probability

Year:

2007

Language:

english

File:

PDF, 1.83 MB

english, 2007

11

STRONG CONVERGENCE OF AN EXPLICIT NUMERICAL METHOD FOR SDES WITH NONGLOBALLY LIPSCHITZ CONTINUOUS COEFFICIENTS

Martin Hutzenthaler, Arnulf Jentzen and Peter E. Kloeden

Journal:

The Annals of Applied Probability

Year:

2012

Language:

english

File:

PDF, 2.11 MB

english, 2012

12

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 and Peter E. Kloeden

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2011

Language:

english

File:

PDF, 1.08 MB

english, 2011

13

Interacting diffusions and trees of excursions: convergence and comparison

Hutzenthaler, Martin

Journal:

Electronic Journal of Probability

Year:

2012

Language:

english

File:

PDF, 731 KB

english, 2012

14

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

Hutzenthaler, Martin, Jentzen, Arnulf, Kloeden, Peter E.

Journal:

The Annals of Applied Probability

Year:

2012

Language:

english

File:

PDF, 366 KB

english, 2012

15

Ergodic behavior of locally regulated branching populations

Hutzenthaler, M., Wakolbinger, A.

Journal:

The Annals of Applied Probability

Year:

2007

Language:

english

File:

PDF, 327 KB

english, 2007

16

Time reversal of some stationary jump diffusion processes from population genetics

Hutzenthaler, Martin, Taylor, Jesse Earl

Journal:

Advances in Applied Probability

Year:

2010

Language:

english

File:

PDF, 281 KB

english, 2010

17

Mini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions

Hutzenthaler, Martin, Lang, Annika, Szpruch, Lukasz, Yaroslavtseva, Larisa

Journal:

Oberwolfach Reports

Year:

2018

Language:

english

File:

PDF, 451 KB

english, 2018

18

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

E, Weinan, Hutzenthaler, Martin, Jentzen, Arnulf, Kruse, Thomas

Journal:

Journal of Scientific Computing

Year:

2019

File:

PDF, 755 KB

2019

19

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

E, Weinan, Hutzenthaler, Martin, Jentzen, Arnulf, Kruse, Thomas

Journal:

Journal of Scientific Computing

Year:

2019

Language:

english

File:

PDF, 755 KB

english, 2019

20

Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities

Hutzenthaler, Martin, Kruse, Thomas

Journal:

SIAM Journal on Numerical Analysis

Year:

2020

File:

PDF, 474 KB

2020

21

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

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

Journal:

SN Partial Differential Equations and Applications

Year:

2020

File:

PDF, 1.33 MB

2020

22

Convergence in HÃ¶lder norms with applications to Monte Carlo methods in infinite dimensions

Cox, Sonja, Hutzenthaler, Martin, Jentzen, Arnulf, van Neerven, Jan, Welti, Timo

Journal:

IMA Journal of Numerical Analysis

Year:

2020

File:

PDF, 654 KB

2020