Almost periodic solutions for stochastic differential equations with exponential dichotomy driven by Levy noise

2014/04/26 by Yan Wang, Wang Yan, Wang, Yan
Economics, Econometrics and Finance · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.1404.6621

20 pages

arxiv created 2014/04/26 · openalex publication_date 2014/04/26 · arxiv updated 2014/04/29 · openalex created_date 2016/10/28 · openalex updated_date 2026/07/28

Abstract

In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by Lévy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and uniqueness of bounded solutions. Furthermore, this unique bounded solution is almost periodic in distribution under slightly stronger conditions. We also give two examples to illustrate our results.

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