Lévy过程驱动的随机发展方程的几乎自守解

摘要

本文介绍了泊松p-期望几乎自守随机过程的概念,在非Lipschitz条件下给出了泊松p-期望几乎自守函数的一个分解定理;在此基础上,运用所得结果研究了一类由Lévy过程驱动的随机发展方程,给出了此类方程均方几乎自守解存在的充分条件并举例说明所得结果的有效性.%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 Lévy 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.