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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.\nA detailed analysis
of the jumps further reveals that the strong law of large numbers can be re
covered on discrete sequences of time points increasing to infinity. This l
eads to a necessary and sufficient condition that depends on the Lévy measu
re of the noise and the growth and concentration properties of the sequence
at the same time.\nFinally, we show that our results generalize to the sto
chastic heat equation with a multiplicative nonlinearity that is bounded aw
ay from zero and infinity.\n\nThis is joint work with Carsten Chong (EPFL,
Lausanne).
DTSTAMP:20210919T101440Z
DTSTART;TZID=Europe/Budapest:20180912T140000
DTEND;TZID=Europe/Budapest:20180912T160000
SEQUENCE:1
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