See by year See by month Jump to month

Kevei Péter: The almost sure asymptotic behavior of the stochastic heat equation with Lévy noise

Download as iCal file
Wednesday, 12. September 2018, 14:00 - 16:00
Abstract: We examine the almost sure asymptotics of the stochastic heat equation with additive Lévy noise. When a spatial point is fixed, and time tends to infinity, we show that the solution develops unusually high peaks over short time intervals, leading to a break down of an intuitively expected strong law of large numbers. More precisely, if we normalize the solution by an increasing nonnegative function, we either obtain convergence to 0, or the limit superior and/or inferior will be infinite.
A detailed analysis of the jumps further reveals that the strong law of large numbers can be recovered on discrete sequences of time points increasing to infinity. This leads to a necessary and sufficient condition that depends on the Lévy measure of the noise and the growth and concentration properties of the sequence at the same time.
Finally, we show that our results generalize to the stochastic heat equation with a multiplicative nonlinearity that is bounded away from zero and infinity.

This is joint work with Carsten Chong (EPFL, Lausanne).
Location : Szeged, Aradi vértanúk tere 1., Riesz terem


JEvents v3.1.8 Stable   Copyright © 2006-2013