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Polynomial stability of exact solution and modified truncated Euler-Maruyamamethod for stochastic differential equations with time-dependent delay areinvestigated in this paper. By using the well known discrete semimartingaleconvergence theorem, sufficient conditions are obtained for both bounded andunbounded delay $\delta$ to ensure the polynomial stability of thecorresponding numerical approximation. Examples are presented to illustrate theconclusion.

Polynomial stability of exact solution and a numerical method for stochastic differential equations with time-dependent delay