p-th Besicovitch Almost Periodic Solutions in Distribution for Semi-linear Non-autonomous Stochastic Evolution Equations

This paper considers p-th Besicovitch almost periodic solutions in distribution for a class of semi-linear non-autonomous stochastic evolution equations in a real separable Hilbert space. The existence and stability of p-th Besicovitch almost periodic solutions in distribution are studied mainly by applying theory of evolution operator, Banach fixed point theorem and some inequality techniques. As the space composed of p-th Besicovitch almost periodic stochastic processes in distribution has no linear structure, it is first proved by Banach fixed point theorem that the equation has a unique L^p -bounded and uniformly L^p -continuous solution, and then, this solution is further verified to be p-th Besicovitch almost periodic in distribution. Moreover, the p-th Besicovitch almost periodic solution in distribution is also shown to be globally exponentially stable. Finally, an example is given to illustrate the obtained results.