摘要：
There are two common approaches in stochastic partial differential equations (SPDE). One is to think of SPDE as a stochastic differential equation with values in a Hilbert space, the other one introduced by J. Walsh in 1986 is more probabilistic. Nowadays SPDE is one of the most important topics in probability. We consider the following stochastic heat equation: u_t=ku_xx+sigma(u)F, where sigma is globally Lipschitz continuous and F is a Gaussian noise. In this talk, I will make sense solutions and we will discuss mathematical intermittency and how do initial data, k and F effect the fluctuations. This is joint work with Daniel Conus, Matthew Joseph and Davar Khoshnevisan.