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We continue our study of the distribution of the maximal number $X^{\ast}_k$ of offsprings amongst all individuals in a critical Galton-Watson process started with $k$ ancestors, treating the case when the reproduction law has a regularly…

Probability · Mathematics 2012-09-19 Jean Bertoin

We are interested in the genealogical structure of alleles for a Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small.…

Probability · Mathematics 2009-06-25 Jean Bertoin

We consider a branching system consisting of particles moving according to a Markov family in $\Rd$ and undergoing subcritical branching with a constant rate $V>0$. New particles immigrate to the system according to homogeneous space-time…

Probability · Mathematics 2009-11-04 Piotr Milos

We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as…

Probability · Mathematics 2007-05-23 Zhiyi Chi

This paper generalizes the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. Inspired by the method of approximation using models with…

Probability · Mathematics 2023-09-19 Likai Jiao

In this paper we consider two related stochastic models. The first one is a branching system consisting of particles moving according to a Markov family in R^d and undergoing subcritical branching with a constant rate of V>0. New particles…

Probability · Mathematics 2012-11-27 Piotr Milos

We derive a complete left-tail asymptotic series for the density of the {\it martingale limit} of a Galton-Watson process with immigration. We show that the series converges everywhere, not only for small arguments. This is the first…

Probability · Mathematics 2025-06-05 Anton A Kutsenko

Skeletons of branching processes are defined as trees of lineages characterized by an appropriate signature of future reproduction success. In the supercritical case a natural choice is to look for the lineages that survive forever. In the…

Probability · Mathematics 2013-04-02 Serik Sagitov , Maria C. Serra

We consider here multitype Bienaym\'e--Galton--Watson trees, under the conditioning that the numbers of vertices of given type satisfy some linear relations. We prove that, under some smoothness conditions on the offspring distribution…

Probability · Mathematics 2023-10-20 Paul Thévenin

This work provides a brief introduction to continuous-state branching processes (CB-processes) and continuous-state branching processes with immigration (CBI-processes) accessible to graduate students with reasonable background in…

Probability · Mathematics 2019-01-14 Zenghu Li

We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…

Probability · Mathematics 2014-04-16 Wei Su

We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienayme-Galton-Watson branching process. More specifically, we are…

Populations and Evolution · Quantitative Biology 2019-09-04 Conrad J. Burden , Albert C. Soewongsono

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…

Probability · Mathematics 2007-05-23 Lea Popovic

Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…

Probability · Mathematics 2019-01-29 Elizaveta Ermakova , Polina Makhmutova , Elena Yarovaya

The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…

Probability · Mathematics 2024-07-02 Jochen Blath , Felix Hermann , Martin Slowik

Consider a branching random walk, where the branching mechanism is governed by a Galton-Watson process, and the migration by a finite range symmetric irreducible random walk on the integer lattice $\mathbb{Z}^d$. Let $Z_n(z)$ be the number…

Probability · Mathematics 2021-06-09 Zhi-qiang Gao

We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton--Watson branching processes. This algorithm is based on a particular discretization of a well-known functional equation that characterizes the…

Numerical Analysis · Mathematics 2020-01-27 Sophie Hautphenne , Stefano Massei

Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…

Probability · Mathematics 2018-11-22 Dmitry Dolgopyat , Pratima Hebbar , Leonid Koralov , Mark Perlman

We consider Galton-Watson branching processes with countable typeset $\mathcal{X}$. We study the vectors ${\bf q}(A)=(q_x(A))_{x\in\mathcal{X}}$ recording the conditional probabilities of extinction in subsets of types $A\subseteq…

Probability · Mathematics 2020-11-23 Daniela Bertacchi , Peter Braunsteins , Sophie Hautphenne , Fabio Zucca

In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of different types. We assume that this function is superadditive,…

Probability · Mathematics 2022-06-22 Coralie Fritsch , Denis Villemonais , Nicolás Zalduendo