Abstract

In this talk, I will review our recent results on the long-term behavior of the solutions to the parabolic and hyperbolic Anderson models. The talk will consist of two parts. The first part concerns the existence and uniqueness of the solutions to the (fractional) heat equation and wave equation driven by multiplicative Gaussian noise, and the Feynmnan-Kac formula for stochastic heat equation. The second part deals with moments Lyapunov exponents for the solutions to the (fractional) Anderson models.