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UID:4cnopleorjcuq30dniand84em9@google.com
CATEGORIES:{lang hu}Sztochasztika szeminárium{/lang}{lang en}Stochastics seminar{/lang}
SUMMARY:Pap Gyula (SZTE): Almost sure, L1- and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration
LOCATION:Szeged, Aradi vértanúk tere 1., Riesz terem.
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Under a first order moment condition on the immigration mechanism
, we show that an appropriately scaled supercritical and irreducible multi-
type continuous state and continuous time branching process with immigratio
n (CBI process) converges almost surely. If an x*log(x) moment condition on
the branching mechanism does not hold, then the limit is zero. If this x*l
og(x) moment condition holds, then we prove L1 convergence as well. The pro
jection of the limit on any left non-Perron eigenvector of the branching me
an matrix is vanishing. If, in addition, a suitable extra power moment cond
ition on the branching mechanism holds, we provide the correct scaling for
the projection of a CBI process on certain left eigenvectors of the branchi
ng mean matrix in order to have almost sure and L1 limit. Moreover, under a
second moment condition on the branching and immigration mechanisms, we pr
ove L2 convergence as well. A representation of the limits is also provided
. (Joint work with Mátyás Barczy and Sandra Palau.)
DTSTAMP:20210126T071756Z
DTSTART;TZID=Europe/Budapest:20180314T140000
DTEND;TZID=Europe/Budapest:20180314T160000
SEQUENCE:0
TRANSP:OPAQUE
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