Kevei Péter (Bolyai Institute, Szeged): On the solution to the stochastic heat equation with Lévy noise

Bécs-Budapest Valószínűségszámítási Szeminárium

Abstract: We examine the almost sure asymptotics of the solution to the stochastic heat equation driven by a Lévy space-time white noise. For fixed time and space we determine the exact tail behavior of the solution. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short time intervals, even in the case of additive noise, which leads to a breakdown of an intuitively expected strong law of large numbers. We also determine the almost sure growth rate in space for fixed time. This is joint work with Carsten Chong (Columbia University).

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