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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.

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
Full Text: DOI
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