Stability in the small moment sense of the backward Euler-Maruyama method for stochastic differential equations with super-linear coefficients
Stability in the small moment sense of the backward Euler-Maruyama method for stochastic differential equations with super-linear coefficients
复制标题
DOI：
10.1016/j.aml.2022.108543
复制
发表时间：
2022-12
期刊：
影响因子：
--
通讯作者：
Xiaotong Li;Wei Liu;Yudong Wang;Ruoxue Wu
中科院分区：
文献类型：
--
作者：
Xiaotong Li;Wei Liu;Yudong Wang;Ruoxue Wu
对于具有超线性漂移系数和扩散系数的随机微分方程，采用后向欧拉-丸山（BEM）方法再现了底层随机微分方程的稳定性。证明了某小点p∈(0,1)的p阶矩指数稳定性和边界元法的指数稳定性。本文部分推广了Higham、Mao和Yuan（2007）的研究结果。数值模拟验证了理论结果。
For stochastic differential equations (SDEs) with super-linear drift and diffusion coefficients, the backward Euler–Maruyama (BEM) method is considered to reproduce the stability of the underlying SDEs. The p th moment exponential stability for some small p∈(0, 1) and the almost sure exponential stability of the BEM method are proved. The results in this paper partially extend those in Higham, Mao and Yuan (2007). Numerical simulations are provided to illustrate the theoretical results.