Mean-square stability properties of an adaptive time-stepping SDE solver

Authors:
H. Lamba;T. Seaman
Affiliations:
Department of Mathematical Sciences, George Mason University, Fairfax, VA;Department of Mathematical Sciences, George Mason University, Fairfax, VA
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We consider stability properties of a class of adaptive time-stepping schemes based upon the Milstein method for stochastic differential equations with a single scalar forcing. In particular, we focus upon mean-square stability for a class of linear test problems with multiplicative noise. We demonstrate that desirable stability properties can be induced in the numerical solution by the use of two realistic local error controls, one for the drift term and one for the diffusion.