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Barczy Mátyás: Asymptotic behaviour of critical decomposable 2-type Galton-Watson processes with immigration

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Thursday, 8. April 2021, 14:00 - 16:00
Abstract: We study the asymptotic behaviour of a critical 2-type 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 processes formed from a critical decomposable 2-type Galton-Watson process with immigration converges weakly. The limit process can be described using one or two independent squared Bessel processes and possibly the unique stationary distribution of an appropriate singe-type subcritical Galton-Watson process with immigration. Our results complete and extend the results of Foster 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 a diffusion process.
This is a joint work with Daniel Bezdany and Gyula Pap.
Location : https://jitsi.math.u-szeged.hu/BolyaiIntezet282

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