Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion

被引：38

作者：

Garrido-Atienza, Maria J. ^{[1
]}

Kloeden, Peter E. ^{[2
]}

Neuenkirch, Andreas ^{[2
]}

机构：

[1] Univ Seville, Dpto Ecuac Diferenciales & Anal Numer, E-41080 Seville, Spain

[2] Univ Frankfurt, Inst Math, D-60325 Frankfurt, Germany

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2009年 / 60卷 / 02期

关键词：

Fractional Brownian motion; Random dynamical system; Random attractor; One-sided dissipative Lipschitz condition; Implicit Euler scheme; DIFFERENTIAL-EQUATIONS DRIVEN; APPROXIMATION; CONVERGENCE;

D O I：

10.1007/s00245-008-9062-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases.

引用

页码：151 / 172

页数：22

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