Penalization of Galton–Watson processes

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 c...

Full description

Saved in:
Bibliographic Details
Published in:Stochastic processes and their applications 2020-05, Vol.130 (5), p.3095-3119
Main Authors: Abraham, Romain, Debs, Pierre
Format: Article
Language:English
Subjects:
Conditioning
Galton–Watson trees
Mathematics
Penalization
Probability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2019.09.005