Beyond the Q-process: various ways of conditioning the multitype Galton-Watson processReportar como inadecuado




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* Corresponding author 1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

Abstract : Conditioning a multitype Galton-Watson process to stay alive into the indefinite future leads to what is known as its associated Q-process. We show that the same holds true if the process is conditioned to reach a positive threshold or a non-absorbing state. We also demonstrate that the stationary measure of the Q-process, obtained by construction as two successive limits first by delaying the extinction in the original process and next by considering the long-time behavior of the obtained Q-process, is as a matter of fact a double limit. Finally, we prove that conditioning a multitype branching process on having an infinite total progeny leads to a process presenting the features of a Q-process. It does not however coincide with the original associated Q-process, except in the critical regime.

Keywords : Multitype branching process Conditioned limit theorem Quasi- stationary distribution Q-process Size-biased distribution Total progeny





Autor: Sophie Pénisson -

Fuente: https://hal.archives-ouvertes.fr/



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