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Poisson $S^2$-almost automorphy for stochastic processes and its applications to SPDEs driven by Lévy noise

The second author is supported by the Fundamental Research Funds for the Central universities (2012017yjsy139)
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  • In this paper, we introduce and study the concepts and properties of Poisson Stepanov-like almost automorphy (or Poisson $S^2$-almost automorphy) for stochastic processes. With appropriate conditions, we apply the results obtained to investigate the asymptotic behavior of the soulutions to SPDEs driven by Lévy noise under $S^2$-almost automorphic coefficients without global Lipschitz conditions. Moreover, the local asymptotic stability of the solutions under local Lipschitz condition is discussed and the attractive domain is also given. Finally, an illustrative example is provided to justify the practical usefulness of the established theoretical results.

    Mathematics Subject Classification: Primary: 34C27, 34D23, 34F05; Secondary: 60H30.

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