Related papers: Subcritical branching processes in random environm…
We study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the…
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…
This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…
In this paper, we consider the subcritical branching random walk in a random environment. We assume the branching and the step jump are independent; and the branching is in random envirenment, i.e., the particles in generation $n$ produce…
We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring…
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 consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
In this paper, we consider a critical Galton-Watson branching process with immigration stopped at zero $\mathbf{W}$. Some precise estimation on the generation function of the $n$-th population are obtained, and the tail probability of the…
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…
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 consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…
In this paper, we study critical and subcritical branching $\alpha$-stable processes, $\alpha \in (0, 2)$. We obtain the exact asymptotic behaviors of the tails of the maximal positions of all subcritical branching $\alpha$-stable processes…
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…
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…
This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and…
In this paper we analyze a branching process with immigration defined recursively by $X_t=\theta_t\circ X_{t-1}+B_t$ for a sequence $(B_t)$ of i.i.d. random variables and random mappings $ \theta_t\circ x:=\theta_t(x)=\sum_{i=1}^xA_i^{(t)},…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…
We establish recurrence and transience criteria for critical branching processes in random environment with immigration. These results are then applied to discuss recurrence and transience of a recurrent random walk in a random environment…