Approximation of stationary solutions to SDEs driven by multiplicative fractional noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Cohen, Serge¹  Panloup, Fabien¹  Tindel, Samy² 

[1] Univ Toulouse 3, Univ Toulouse 2, Univ Toulouse 1, INSA,IMT,CNRS UMR 5219, F-31062 Toulouse, France

[2] Univ Lorraine, Inst Elie Cartan Lorraine, F-54506 Vandoeuvre Les Nancy, France

关键词: Stochastic differential equation;    Fractional Brownian motion;    Stationary process;    Euler scheme;   

DOI  :  10.1016/j.spa.2013.11.004

来源: Elsevier

【 摘 要 】

In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a fractional Brownian motion with Hurst parameter H > 1/2 and obtain some (functional) convergence properties of some empirical measures of the Euler scheme to the stationary solutions of such SDEs. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free