Related papers: Simulations and a conditional limit theorem for in…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…
We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of…
We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the one-dimensional situation, to the strongly subcritical case.…
We consider branching process evolving in i.i.d. random environment. It is assumed that the process is intermediately subcritical. We investigate the initial stage of the evolution of the process given its survival for a long time.
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…
We introduce a branching process in a sparse random environment as an intermediate model between a Galton--Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and…
Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
A critical branching process $\left\{ Z_{k},k=0,1,2,...\right\} $ in a random environment is considered. A conditional functional limit theorem for the properly scaled process $\left\{ \log Z_{pu},0\leq u<\infty \right\} $ is established…
In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the…
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…
In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…
A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type…
We study the asymptotics of the survival probability for the critical and decomposable branching processes in random environment and prove Yaglom type limit theorems for these processes. It is shown that such processes possess some…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to 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…
Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution…