均方权伪概自守发展方程及其应用(英文)

Mean-square Weighted Pseudo Almost Automorphic Evolution Equation and its Applications

本文首先引入均方权伪概自守随机过程的概念,并在Lipchitz条件下得到一个均方权伪概自守随机过程的分解定理.通过利用算子半群发展簇理论,Babach不动点定理和随机分析技巧,本文得到Hilbert空间上的一类随机发展方程的均方权伪概自守温和解的存在唯一性和稳定性结论.

In this paper, the concept of the mean-square weighted pseudo almost automorphic for a stochastic process is introduced. We establish a composition theorem for mean-square weighted pseudo almost automorphic stochastic process under a Lipschitz conditions. By applying the theory of the semigroups of the operators to an evolution family,Banach fixed point theorem and the tech- niques of stochastic analysis, we investigate the existence, the uniqueness and the stability of a mean- square weighted pseudo almost automorphic mild solution for a stochastic evolution equation in Hil- bert space.