An SPDE with the laws of Levy processes as its invariant measures
Seminar Room 1, Newton Institute
It is well known that the Wiener measure is the invariant measure of the stochastic heat equation driven by a space-time Gaussian noise. Hence, it is natural to ask to whether the law of one dimensional Levy process will be invariant under a stochastic heat equation? In this talk, we will first construct a singular noise and then consider a linear heat equation on a half line with this noise to answer the above question. Our assumption on the corresponding Levy measure is very mild to show that the distributions of Levy processes are the only invariant measures of the stochastic heat equation.