Related papers: Subcritical branching processes in random environm…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${\mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that…
Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a L\'evy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In…
Using the annealed approach we investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in i.i.d. random environment. We show under rather general assumptions on the form of the…
We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. For the case where the…
Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough…
We first study a model, introduced recently in \cite{ES}, of a critical branching random walk in an IID random environment on the $d$-dimensional integer lattice. The walker performs critical (0-2) branching at a lattice point if and only…
We introduce a random barrier to a supercritical branching random walk in an i.i.d. random environment $\{\mathcal{L}_n\}$ indexed by time $n,$ i.e., in each generation, only the individuals born below the barrier can survive and reproduce.…
We consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…
Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…
We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…
The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions…
Consider a discrete-time supercritical discounted branching random walk, in which increments at depth $k$ are independent and identically distributed with the same law as $m^{-kH}Y$, where $Y$ has a fixed law, $H>0$, and $m>1$ is the…
We consider branching random walk in random environment (BRWRE) and prove the existence of deterministic subsequences along which their maximum, centered at its mean, is tight. This partially answers an open question in arXiv:1711.00852.…
We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours…
A Galton-Watson process in varying environment is a discrete time branching process where the offspring distributions vary among generations. Based on a two-spine decomposition technique, we provide a probabilistic argument of a Yaglom-type…