In this paper, we introduce a concept of Poisson $p$-mean almost automorphy for stochastic processes and give the composition theorems for (Poisson) $p$-mean almost automorphic functions under non-Lipschitz conditions. Our abstract results are, subsequently, applied to study a class of neutral stochastic evolution equations driven by L\'evy noise, and we present sufficient conditions for the existence of square-mean almost automorphic mild solutions. An example is provided to illustrate the effectiveness of the proposed result.
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CUI Jing;SHEN GuangJun. Almost Automorphic Solutions to Stochastic Evolution Equations Driven by L\'evy Processes. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2017, 33(5): 450-466.