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Journal Articles Stochastic Processes and their Applications Year : 2020

## Penalization of Galton-Watson processes

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Romain Abraham
Pierre Debs

#### 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.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-01744802 , version 1 (27-03-2018)

### Identifiers

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

### Cite

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

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