On stability of numerical solutions of neutral stochastic delay differential equations with time-dependent delay. (English) Zbl 07783910
Summary: This paper focuses on exponential stability of numerical solutions of neutral stochastic delay differential equations. A novel approach is introduced to study numerical approximation methods of neutral stochastic differential equations with time-dependent delay. In contrast to the advances in the literature, this work provides a new method and new criteria for which the Euler-Maruyama approximation method and the backward Euler-Maruyama approximation method can reproduce exponential stability in mean square and almost sure exponential stability for sufficiently small step sizes. Two examples are provided to demonstrate the effectiveness of our criteria.
{© 2023 John Wiley & Sons, Ltd.}
{© 2023 John Wiley & Sons, Ltd.}
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 34K50 | Stochastic functional-differential equations |
| 34K40 | Neutral functional-differential equations |
Keywords:
almost sure exponential stability; backward Euler-Maruyama approximation; Euler-Maruyama approximation; exponential stability in mean square; neutral stochastic delay differential equationsReferences:
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