Speaker : Dr. Shang-Yuan Shiu(Institute of Mathematics, Academia Sinica)
Title : On the stochastic heat equations.
Time : 2012-02-06 (Mon) 14:10 -
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
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.