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UID:0povcl12rsa5fk93m9aifrgvk2@google.com
CATEGORIES:{lang hu}Sztochasztika szeminárium{/lang}{lang en}Stochastics seminar{/lang}
SUMMARY:Kevei Péter: The almost sure asymptotic behavior of the stochastic heat equation with Lévy noise
LOCATION:Szeged, Aradi vértanúk tere 1., Riesz terem
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract: We examine the almost sure asymptotics of the stochastic heat equ
ation with additive Lévy noise. When a spatial point is fixed, and time ten
ds to infinity, we show that the solution develops unusually high peaks ove
r short time intervals, leading to a break down of an intuitively expected
strong law of large numbers. More precisely, if we normalize the solution b
y an increasing nonnegative function, we either obtain convergence to 0, or
the limit superior and/or inferior will be infinite.

A detailed analys
is of the jumps further reveals that the strong law of large numbers can be
recovered on discrete sequences of time points increasing to infinity. Thi
s leads to a necessary and sufficient condition that depends on the Lévy me
asure of the noise and the growth and concentration properties of the seque
nce at the same time.

Finally, we show that our results generalize to t
he stochastic heat equation with a multiplicative nonlinearity that is boun
ded away from zero and infinity.

This is joint work with Carsten C
hong (EPFL, Lausanne).
DTSTAMP:20210508T012325Z
DTSTART;TZID=Europe/Budapest:20180912T140000
DTEND;TZID=Europe/Budapest:20180912T160000
SEQUENCE:1
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