Stochastic parabolic equations in bounded domains: random evolution operator and lyapunov exponents

Abstract

We consider linear second order stochastic partial differential equations with finitely many noise sources. A stochastic Feynman-Kac-type representation of mild solutions yields the existence of random evolution operators (fundamental solutions). Integrability properties and compactness for them are proved. Finally, the existence of Lyapunov exponents is established