**Abstract:** |
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 the most important
topic 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, we will discuss the
moment estimations, 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. |