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.
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页数：15
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