Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
Artikel i vetenskaplig tidskrift, 2017

The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential equations and necessary and sufficient conditions ensuring mean-square stability are given. They are applied to typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler–Maruyama, Milstein, Crank–Nicolson, and forward and backward Euler methods. Furthermore, results on the relation to stability properties of corresponding analytical solutions are provided. Simulations of the stochastic heat equation illustrate the theory.

rational approximations

Lévy processes

spectral methods

Galerkin methods

finite element methods

Milstein scheme

linear stochastic partial differential equations

Euler–Maruyama scheme

Asymptotic mean-square stability

numerical approximations of stochastic differential equations

Författare

Annika Lang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Andreas Petersson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Andreas Thalhammer

BIT Numerical Mathematics

0006-3835 (ISSN) 1572-9125 (eISSN)

Vol. 57 4 963-990

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

DOI

10.1007/s10543-017-0684-7

Mer information

Skapat

2017-11-28