Kevei Péter (Szeged): Intermittency and almost sure properties of the solution of the stochastic heat equation with Lévy noise

We investigate the moment asymptotics of the solution to the stochastic heat equation driven by a $(d+1)$-dimensional Lévy space--time white noise. Unlike the case of Gaussian noise, the solution typically has no finite moments of order $1+2/d$ or higher. Intermittency of order $p$, that is, the exponential growth of the $p$th moment as time tends to infinity, is established in dimension $d=1$ for all values $p\in(1,3)$, and in higher dimensions for some $p\in(1,1+2/d)$. In some special cases we also investigate the almost sure properties of the solution. The talk is based on ongoing joint work with Carsten Chong.