Polynomial and exponential stability of $\theta$-EM approximations to a class of stochastic differential equations

Abstract

Both the mean square polynomial stability and exponential stability of $\theta$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\le \theta \le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.

arXiv comment18 pages

References in corpus (2)

• $V$-Integrability, Asymptotic Stability And Comparison Theorem of Explicit Numerical Schemes for SDEs
• Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations

Cited by in corpus (1)

• Exponential stability of the exact solutions and $\theta$-EM approximations to neutral SDDEs with Markov switching