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.
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页码：151 / 172
页数：22
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