Related papers: Small value probabilities for supercritical branch…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
We consider a class of multitype Galton-Watson branching processes with a countably infinite type set $\mathcal{X}_d$ whose mean progeny matrices have a block lower Hessenberg form. For these processes, the probability $\boldsymbol{q}(A)$…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
Let $(Z_n,n\geq 0)$ be a supercritical Galton-Watson process whose offspring distribution $\mu$ has mean $\lambda>1$ and is such that $\int x(\log(x))_+ d\mu(x)<+\infty$. According to the famous Kesten \& Stigum theorem, $(Z_n/\lambda^n)$…
Let $(Z_{n})$ be a supercritical branching process in a random environment $\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\mathbb{E}[Z_{n}|\xi ]$. We show large and moderate deviation principles for the sequence $\log…
A decomposable strongly critical Galton-Watson branching process with $N$ types of particles labelled $1,2,...,N$ is considered in which a type~$i$ parent may produce individuals of types $j\geq i$ only. This model may be viewed as a…
The current paper focuses on studying the impact of immigration with an infinite mean, driven by a discrete-stable compound Poisson process, when it is entering the branching environment with infinite variance of reproduction. Our goal is…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk…
Given a super-critical Galton-Watson process $\{Z_n\}$ and a positive sequence $\{\epsilon_n\}$, we study the limiting behaviors of $P(S_{Z_n}/Z_n\geq\epsilon_n)$ and $P(S_{Z_n}/m^n\geq\epsilon_n) $ with sums $S_{n}$ of i.i.d. random…
We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi$. We study the convergence rates of the martingale $W_n = Z_n/ E[Z_n| \xi]$ to its limit $W$. The following results about the convergence almost sur (a.s.), in…
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…
Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Let $\{Z_n^i = (Z_n^i(r))_{1 \le r \le d}: n \ge 0\}$ be a supercritical $d$-type branching process in an i.i.d. environment $\xi = (\xi_0, \xi_1, \dots)$, starting from a single particle of type $i$. The offspring distribution at…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…