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UID:6ihqf5euuumddboihijmogdgmj@google.com
CATEGORIES:{lang hu}Sztochasztika szeminárium{/lang}{lang en}Stochastics seminar{/lang}
SUMMARY:Barczy Mátyás: Asymptotic behaviour of critical decomposable 2-type Galton-Watson processes with immigration
LOCATION:https://jitsi.math.u-szeged.hu/BolyaiIntezet282
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract: We study the asymptotic behaviour of a critical 2-ty
pe Galton-Watson process with immigration when its offspring mean matrix is
reducible, in other words, when the process is decomposable. It is proved
that, under second or fourth order moment assumptions on the offspring and
immigration distributions, a sequence of appropriately scaled random step p
rocesses formed from a critical decomposable 2-type Galton-Watson process w
ith immigration converges weakly. The limit process can be described using
one or two independent squared Bessel processes and possibly the unique sta
tionary distribution of an appropriate singe-type subcritical Galton-Watson
process with immigration. Our results complete and extend the results of F
oster and Ney for some strongly critical decomposable 2-type Galton-Watson
processes with immigration. In the proofs we use limit theorems for random
step processes created from martingale differences towards&
nbsp;a diffusion process.
This
is a joint work with Daniel Bezdany and&
nbsp;Gyula Pap.
DTSTAMP:20240329T092723Z
DTSTART;TZID=Europe/Budapest:20210408T140000
DTEND;TZID=Europe/Budapest:20210408T160000
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