Equivalence of the mean square stability between the partially truncated Euler-Maruyama method and stochastic differential equations with super-linear growing coefficients

被引：2

作者：

Jiang, Yanan ^{[1
]}

Huang, Zequan ^{[2
]}

Liu, Wei ^{[1
]}

机构：

[1] Shanghai Normal Univ, Shanghai, Peoples R China

[2] Hefei Univ Technol, Hefei, Anhui, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

基金：

中国国家自然科学基金;

关键词：

Partially truncated Euler-Maruyama method; Stochastic differential equations; Mean square exponential stability; Super-linear growing coefficients; LIPSCHITZ CONTINUOUS COEFFICIENTS; EXPONENTIAL STABILITY; DELAY EQUATIONS; CONVERGENCE; SCHEME; APPROXIMATIONS; RATES; SDES;

D O I：

10.1186/s13662-018-1818-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For stochastic differential equations (SDEs) whose drift and diffusion coefficients can grow super-linearly, the equivalence of the asymptotic mean square stability between the underlying SDEs and the partially truncated Euler-Maruyama method is studied. Using the finite time convergence as a bridge, a twofold result is proved. More precisely, the mean square stability of the SDEs implies that of the partially truncated Euler-Maruyama method, and the mean square stability of the partially truncated Euler-Maruyama method indicates that of the SDEs given the step size is carefully chosen.

引用

页数：15

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