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

摘要

In this article, we study almost automorphic solutions for semilinear stochastic differential equations driven by Levy 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.