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arXiv · 1407.1486

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

Yunjiao Hu·Guangqiang Lan·Chong Zhang
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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.

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Yunjiao Hu, Guangqiang Lan, Chong Zhang. 2014-07-06. Polynomial and exponential stability of $\theta$-EM approximations to a class of stochastic differential equations. https://arxiv.org/abs/1407.1486

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