Stability and error analysis of an implicit Milstein finite difference scheme for a two-dimensional Zakai SPDE

Author: 

Reisinger, C
Wang, Z

Publication Date: 

18 June 2019

Journal: 

BIT Numerical Mathematics

Last Updated: 

2020-08-25T15:13:38.91+01:00

Issue: 

2019

DOI: 

10.1007/s10543-019-00761-8

page: 

1-43

abstract: 

This article proposes an implicit finite difference scheme for a two-dimensional parabolic stochastic partial differential equation of Zakai type. The scheme is based on a Milstein approximation to the stochastic integral and an alternating direction implicit discretisation of the elliptic term. Mean-square stability and L2 -convergence of first order in time and second order in space are proven by Fourier analysis, in the presence of Dirac initial data. Numerical tests confirm these findings empirically.

Symplectic id: 

994767

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article