Almost automorphic solutions for stochastic differential equations driven by Lévy noise with exponential dichotomy. Issue 2 (4th March 2017)

• Record Type: Journal Article
• Authors: Sun, Kai; Wang, Yan
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 2(2017)
• Page Start: 211
• Page End: 236
• Publication Date: 2017-03-04
• Subjects: Almost automorphic solution -- stochastic differential equation -- exponential dichotomy -- Lévy process; 60H10 -- 34C27 -- 60G51 -- 34G20; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1237878
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this article, we study almost automorphic solutions for semilinear stochastic differential equations driven by Lévy noise. We establish the existence and uniqueness of bounded solutions by using the Banach fixed point theorem, the exponential dichotomy property and stochastic analysis techniques. Furthermore, this unique bounded solution is almost automorphic in distribution under slightly stronger conditions. We also give two examples to illustrate our results.