ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

Abstract

We prove the existence of almost periodic solutions to a class of abstract stochastic evolution equations on a Banach space E, [Formula: see text] Both autonomous (A is a C0-semigroup generator) and non-autonomous (A(t) satisfies conditions of Acquistapace–Terreni and generates a strongly continuous evolution family) cases are studied. Results are based on the theory of stochastic integration on Banach spaces of van Neerven and Weis and R-boundedness estimates for semigroups and evolution families due to Hytönen and Veraar. An example is given for a non-autonomous second order boundary value problem on a domain in ℝd.