相关论文: Survival of branching processes in random environm…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
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 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 a critical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We are interested in the event $\mathcal{A}_i(n)$ that all individuals alive at time $n$ are offspring of the…
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…
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 subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the…
Let $Z_{n}$ be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Branching processes in a random environment are natural generalisations of Galton-Watson processes. In this paper we analyse the asymptotic decay of the survival probability for a sequence of slightly supercritical branching processes in an…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We study the asymptotic behavior of the probability of non extinction of a weakly subcritical multitype branching process in iid random environments. Under suitable assumptions, the survival probability is of order of $\rho^n n ^{-3/2}$ for…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
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 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 consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We study the asymptotic behaviour of the survival probability of a multi-type branching processes in random environment. The class of processes we consider corresponds, in the one-dimensional situation, to the intermediately subcritical…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
Using a high performance computer cluster, we run simulations regarding an open problem about d-dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently,…