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

摘要

In this paper, we study almost periodic solutions for semilinear stochasticdifferential equations driven by L\'{e}vy noise with exponential dichotomyproperty. Under suitable conditions on the coefficients, we obtain theexistence and uniqueness of bounded solutions. Furthermore, this unique boundedsolution is almost periodic in distribution under slightly stronger conditions.We also give two examples to illustrate our results.