Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
Journal article, 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.

finite element methods

rational approximations

spectral methods

Milstein scheme

Euler–Maruyama scheme

Asymptotic mean-square stability

Lévy processes

numerical approximations of stochastic differential equations

linear stochastic partial differential equations

Galerkin methods

Author

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Andreas Petersson

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Andreas Thalhammer

BIT Numerical Mathematics

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

Vol. 57 4 963-990

Subject Categories

Computational Mathematics

Probability Theory and Statistics

DOI

10.1007/s10543-017-0684-7

More information

Latest update

1/17/2022