Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations

Abstract

We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.

Key words： Stochastic evolution equation; μ-pseudo almost automorphic process; fixed point theorem

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