38 citations · 135 across the 9 of their papers we have counts for
9 papers
Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
Matteo Beccari, Martin Hutzenthaler, Arnulf Jentzen +3
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimension…
Counterexamples to regularities for the derivative processes associated to stochastic evolution equations
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial…
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…
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…
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan
In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the…
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…