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

Keywords:

• Stochastic partial differential equations
• Stochastic Feynman-Kac formula
• random evolution operator
• stochastic fundamental solution
• Lyapunov exponents