Stepanov-like almost automorphic solutions for stochastic differential equations with Lévy noise

ABSTRACT

In this paper, we introduce a new concept of Poisson Stepanov-like almost automorphy (or Poisson S²-almost automorphy). Under some suitable conditions on the coefficients, we establish the existence and uniqueness of Stepanov-like almost automorphic mild solution to a class of semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solution. Finally, we give an example to illustrate the theoretical results obtained in this paper.

KEYWORDS:

• Asymptotic stability
• Lévy noise
• Stepanov-like almost automorphy
• stochastic differential equations

MATHEMATICS SUBJECT CLASSIFICATION:

• 60H15
• 60G15
• 60H05

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Funding

This research is partially supported by the NNSF of China [grant number 11571071], and Natural Science Foundation of Hubei Province [grant number 2016CFB479] and China postdoctoral fund (No. 2017M610216).