1.8k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- ETH ZurichCH99 papers
- University of MünsterDE18 papers
- University of PaviaIT9 papers
- University of ViennaAT9 papers
- University of Duisburg-EssenDE7 papers
- Chinese University of Hong Kong, ShenzhenCN6 papers
- Shenzhen Research Institute of Big DataCN6 papers
- University of Maryland, College ParkUS6 papers
- Princeton UniversityUS5 papers
- TU WienAT5 papers
- Austrian Academy of SciencesAT4 papers
- Chalmers University of TechnologySE4 papers
20 papers · 1 filter
Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives
Arnulf Jentzen, Benno Kuckuck, Thomas Müller-Gronbach +1
In the recent article [A. Jentzen, B. Kuckuck, T. Müller-Gronbach, and L. Yaroslavtseva, arXiv:1904.05963 (2019)] it has been proved that the solutions to every additive noise driv…
Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combina…
Existence, uniqueness, and numerical approximations for stochastic Burgers equations
Sara Mazzonetto, Diyora Salimova
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial…
Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform Hölder continuity in time, and strong convergence rates for a…
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
Sebastian Becker, Benjamin Gess, Arnulf Jentzen +1
Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particul…
Approximation methods for piecewise deterministic Markov processes and their costs
Peter Kritzer, Gunther Leobacher, Michaela Szölgyenyi +1
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general co…
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
Sebastian Becker, Benjamin Gess, Arnulf Jentzen +1
The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but,…
On the mild Itô formula in Banach spaces
Sonja Cox, Arnulf Jentzen, Ryan Kurniawan +1
The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& Röckner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math…
On the differentiability of solutions of stochastic evolution equations with respect to their initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan +1
In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the…
Exponential moments for numerical approximations of stochastic partial differential equations
Arnulf Jentzen, Primož Pušnik
Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such app…
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
Martin Hutzenthaler, Arnulf Jentzen, Diyora Salimova
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white n…
Numerical analysis of lognormal diffusions on the sphere
Lukas Herrmann, Annika Lang, Christoph Schwab
Numerical solutions of stationary diffusion equations on the unit sphere with isotropic lognormal diffusion coefficients are considered. Hölder regularity in sense for isotro…
Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise
Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring…
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities
Arnulf Jentzen, Primož Pušnik
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipsch…
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients
Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood i…
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients
Daniel Conus, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are…
Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds
Roman Andreev, Annika Lang
A version of the Kolmogorov-Chentsov theorem on sample differentiability and Hölder continuity of random fields on domains of cone type is proved, and the result is generalized to…
Covariance structure of parabolic stochastic partial differential equations
Annika Lang, Stig Larsson, Christoph Schwab
In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, te…
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
Martin Hutzenthaler, Arnulf Jentzen
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the com…
A mild Ito formula for SPDEs
Giuseppe Da Prato, Arnulf Jentzen, Michael Roeckner
This article introduces a certain class of stochastic processes, which we suggest to call mild Ito processes, and a new - somehow mild - Ito type formula for such processes. Exampl…