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An analysis of stability of Milstein method for stochastic differential equations with delay. (English) Zbl 1136.65009
Summary: This paper deals with the adapted Milstein method for solving linear stochastic delay differential equations. It is proved that the numerical method is mean-square (MS) stable under suitable conditions. The obtained result shows that the method preserves the stability property of a class of linear constant-coefficient problems. This is also verified by several numerical examples.

MSC:
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
34K50Stochastic functional-differential equations
60H35Computational methods for stochastic equations