Asymptotically almost automorphic solutions to stochastic differential equations driven by a Lévy process. Issue 7 (2nd October 2016)

• Record Type: Journal Article
• Authors: Chang, Yong-Kui; Tang, Chao
• Is Part Of: Stochastics. Volume 88:Issue 7(2016)
• Page Start: 980
• Page End: 1011
• Publication Date: 2016-10-02
• Subjects: Poisson asymptotically almost automorphy for stochastic processes -- stochastic differential equations -- Lévy process; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1178748
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper, a new concept of Poisson asymptotically almost automorphy for stochastic processes is introduced. And then, some fundamental properties including composition theorems for the space of such processes are proved. Subsequently, this concept is applied to investigate the existence and uniqueness of asymptotically almost automorphic solutions in distribution to some linear and semilinear stochastic differential equations driven by a Lévy process under some suitable conditions. Finally, an example is given to illustrate the main results.