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

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.

Keywords:

• Almost automorphic solution
• stochastic differential equation
• exponential dichotomy
• Lévy process

Mathematics Subject Classification:

• 60H10
• 34C27
• 60G51
• 34G20