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
11 papers · 1 filter
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…
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces
Adam Andersson, Mario Hefter, Arnulf Jentzen +1
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diff…
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…
Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient
Franziska Weber
We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with Hölder continuous coefficient. The obtained…
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time p…
Statistical solutions of hyperbolic conservation laws I: Foundations
Ulrik Skre Fjordholm, Samuel Lanthaler, Siddhartha Mishra
We seek to define statistical solutions of hyperbolic systems of conservation laws as time-parametrized probability measures on -integrable functions. To do so, we prove the equ…
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions
Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen +2
We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly Hölder continuous in ti…
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…
Analysis and Simulation on a Model for the Evolution of Tumors under the Influence of Nutrient and Drug Application
Konstantina Trivisa, Franziska Weber
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with…
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…