443 citations · 1.2k across the 25 of their papers we have counts for
6 papers · 1 filter
Fokker-Planck equation for stochastic heat equations
Qingyan Meng, Jinqiao Duan, Jinlong Wei +1
This work is devoted to the study of the Fokker--Planck equation for a stochastic heat equation with an additive -Wiener noise and non-homogeneous boundary conditions. We explic…
Strong order-one convergence of the Euler method for random ordinary differential equations driven by semi-martingale noises
Peter E. Kloeden, Ricardo M. S. Rosa
It is well known that the Euler method for a random ordinary differential equation driven by a stochastic process with -…
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…
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,…
Efficient simulation of nonlinear parabolic SPDEs with additive noise
Arnulf Jentzen, Peter Kloeden, Georg Winkel
Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial diff…
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden
The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with superlinearly growing and glob…