Favard separation method for almost periodic stochastic differential equations

Abstract

Favard separation method is an important means to study almost periodic solutions to linear differential equations; later, Amerio applied Favard's idea to nonlinear differential equations. In this paper, by appropriate choosing separation and almost periodicity in distribution sense, we obtain the Favard and Amerio type theorems for stochastic differential equations.

arXiv comment23 pages, no figures; added Theorem 4.7, revised a little argument of the proof of Theorem 3.1