Poisson mu-pseudo almost automorphic stochastic processes and its applications to nonlinear Sobolev-type SDEs with Markov switching

摘要

This paper investigates the equivalence betweenp-mean Poisson mu-pseudo almost automorphic and Poisson asymptotically almost automorphic stochastic processes outside one mu-ergodic zero set and then obtains the completeness of the space of Poisson mu-pseudo almost automorphic stochastic processes without the Lipschitz condition. These properties established enrich the knowledge of Poisson mu-pseudo almost automorphic stochastic processes. Meanwhile, a more significant point is that without the Amerio semiseparation condition, we establish the Amerio-type theorem that all the L-p-bounded mild solutions are mu-pseudo almost automorphic in distribution for a class of nonlinear Sobolev-type stochastic differential equations with Markov switching and jumps. In this sense, we partly contribute to a better understanding of the stochastic analysis between L-p-bounded mild solutions and mu-pseudo almost automorphic mild solutions in distribution for nonlinear SDEs. Finally, we give an example to illustrate the effectiveness of our results.