Penalization of Galton–Watson processes

Romain Abraham and Pierre Debs

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 3095-3119

Abstract: We apply the penalization technique introduced by Roynette, Vallois, Yor for Brownian motion to Galton–Watson processes with a penalizing function of the form P(x)sx where P is a polynomial of degree p and s∈[0,1]. We prove that the limiting martingales obtained by this method are most of the time classical ones, except in the super-critical case for s=1 (or s→1) where we obtain new martingales. If we make a change of probability measure with this martingale, we obtain a multi-type Galton–Watson tree with p distinguished infinite spines.

Keywords: Galton–Watson trees; Penalization; Conditioning (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:5:p:3095-3119

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DOI: 10.1016/j.spa.2019.09.005

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