相关论文: Yaglom's limit for critical Galton-Watson processe…
A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable…
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…
Branching processes $(Z_n)_{n \ge 0}$ in a varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results concern general criteria for a.s. extinction,…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…
We establish a general sufficient condition for a sequence of Galton Watson branching processes in varying environment to converge weakly. This condition extends previous results by allowing offspring distributions to have infinite…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
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…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
In this note we propose a two-spine decomposition of the critical Galton-Watson tree and use this decomposition to give a probabilistic proof of Yaglom's theorem.
We consider a special class of Galton-Watson theta-processes in a varying environment fully defined by four parameters, with two of them $(\theta,r)$ being fixed over time $n$, and the other two $(a_n,c_n)$ characterizing the altering…
Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a…
We investigate Galton--Watson processes in varying environment, for which $\bar f_n \uparrow 1$ and $\sum_{n=1}^\infty (1-\bar f_n) = \infty$, where $\bar f_n$ stands for the offspring mean in generation $n$. Since the process dies out…
We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring…
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…
The classical Galton--Watson process works with a fixed probability of fission at each time step. One of the generalizations is that the probabilities depend on time. We consider one of the most complex and interesting cases when we do not…
We study the evolution of the population size distribution of a critical Galton-Watson process with infinite variance of the offspring size of particles assuming that the population size is unusually small at the distant moment $n$ of…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…