Ergodicity and strong limit results for two-time-scale functional stochastic differential equations. Issue 6 (2nd November 2017)

• Record Type: Journal Article
• Authors: Bao, Jianhai; Song, Qingshuo; Yin, George; Yuan, Chenggui
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 6(2017)
• Page Start: 1030
• Page End: 1046
• Publication Date: 2017-11-02
• Subjects: Two time scale -- functional stochastic differential equation -- exponential ergodicity -- invariant probability measure -- strong limit theorem; 60F17 -- 60F25 -- 60J60 -- 39B72; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1349613
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: This article focuses on a class of two-time-scale functional stochastic differential equations, where the phase space of the segment processes is infinite-dimensional. The systems under consideration have a fast-varying component and a slowly varying one. First, the ergodicity of the fast-varying component is obtained. Then inspired by the Khasminskii's approach, an averaging principle, in the sense of convergence in the p th moment uniformly in time within a finite time interval, is developed.