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.
Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods
Numerical methods for the 2nd moment of stochastic ODEs
A New Methodology for the Development of Numerical Methods for the Numerical Solution of the Schrödinger Equation
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