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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…
Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in…
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…
Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations
Sebastian Becker, Arnulf Jentzen
This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (S…