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Mean square exponential stability of numerical methods for stochastic differential delay equations (2306.12116v1)
Published 21 Jun 2023 in math.NA, cs.NA, and math.PR
Abstract: Mean square exponential stability of $\theta$-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 $\theta$-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.