Mean square exponential stability of numerical methods for stochastic differential delay equations

Guangqiang Lan; Qi Liu

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arXiv · 2306.12116

Mean square exponential stability of numerical methods for stochastic differential delay equations

Guangqiang Lan·Qi Liu

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Abstract

Mean square exponential stability of $θ$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential stability of the $θ$-EM and MTEM methods for SDDEs, which are different from most existing results under Khasminskii-type conditions. Two examples are provided to support our conclusions.

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Guangqiang Lan, Qi Liu. 2023-06-21. Mean square exponential stability of numerical methods for stochastic differential delay equations. https://arxiv.org/abs/2306.12116

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