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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 immigrat
ion mechanism, we show that an appropriately scaled supercritical and irred
ucible multi-type continuous state and continuous time branching process wi
th immigration (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*log(x) moment condition holds, then we prove L1 convergence as
well. The projection of the limit on any left non-Perron eigenvector of the
branching mean matrix is vanishing. If, in addition, a suitable extra powe
r moment condition on the branching mechanism holds, we provide the correct
scaling for the projection of a CBI process on certain left eigenvectors o
f the branching mean matrix in order to have almost sure and L1 limit. More
over, under a second moment condition on the branching and immigration mech
anisms, we prove L2 convergence as well. A representation of the limits is
also provided. (Joint work with Mátyás Barczy and Sandra Palau.)
DTSTAMP:20210621T033013Z
DTSTART;TZID=Europe/Budapest:20180314T140000
DTEND;TZID=Europe/Budapest:20180314T160000
SEQUENCE:0
TRANSP:OPAQUE
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