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arXiv · 1702.07700

Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions

Annika Lang·Andreas Petersson·Andreas Thalhammer
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Abstract

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.

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Annika Lang, Andreas Petersson, Andreas Thalhammer. 2017-02-24. Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions. https://doi.org/10.1007/s10543-017-0684-7

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