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Survival, Malthusian growth and extinction of reinforced Galton Watson processes
Galton-Watson process is a classical stochastic model for describing the evolution of a population over discrete time. In this process, every individual independently produces offspring according to a fixed distribution.
We introduce a reinforced version of the Galton-Watson process, with parameters $\nu$ and $q \in (0,1)$, such that every individual in the process reproduces as follows: with probability $1-q$, it gives birth to children according to the law $\nu$, while with probability $q$ it chooses one of its ancestors uniformly at random and gives birth to the same number of children as that ancestor.
Denoting by $Z_n$ the number of individuals alive at generation $n$ in this process, we study the asymptotic behaviour of $\mathbb E(Z_n)$, give conditions for $\mathbb{P}(Z_n \to \infty) > 0$ and describe the empirical ancestral offspring distribution of individuals at large times.
Date:
17 October 2025, 11:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
TCC VC room
Speaker:
Bastien Mallein (Toulouse)
Organising department:
Department of Statistics
Organisers:
Matthias Winkel (Department of Statistics, University of Oxford),
Julien Berestycki (University of Oxford),
Christina Goldschmidt (Department of Statistics, University of Oxford),
James Martin (Department of Statistics, University of Oxford)
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Public
Editors:
Christina Goldschmidt,
James Martin
