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

06/21/2023

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by   Guangqiang Lan, et al.

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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.