# Penalization of Galton-Watson processes

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 $P (x)s^x$ 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.
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Journal articles
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Cited literature [18 references]

https://hal.archives-ouvertes.fr/hal-01744802
Contributor : Romain Abraham Connect in order to contact the contributor
Submitted on : Tuesday, March 27, 2018 - 4:29:43 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
Long-term archiving on: : Thursday, September 13, 2018 - 10:38:44 AM

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### Identifiers

• HAL Id : hal-01744802, version 1
• ARXIV : 1803.10611

### Citation

Romain Abraham, Pierre Debs. Penalization of Galton-Watson processes. Stochastic Processes and their Applications, Elsevier, 2020, 130, pp.3095-3119. ⟨hal-01744802⟩

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