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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…

Probability · Mathematics 2012-04-11 Vladimir Vatutin , Xinghua Zheng

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…

Probability · Mathematics 2013-12-20 Vincent Bansaye , Vladimir Vatutin

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…

Probability · Mathematics 2013-10-02 Christian Böinghoff , Martin Hutzenthaler

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.…

Probability · Mathematics 2017-11-21 Vladimir Vatutin , Vitali Wachtel

Branching Processes in Random Environment (BPREs) $(Z_n:n\geq0)$ are the generalization of Galton-Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical case, the process…

Probability · Mathematics 2012-10-17 Vincent Bansaye , Christian Boeinghoff

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…

Probability · Mathematics 2012-09-07 V. I. Afanasyev , C. Boeinghoff , G. Kersting , V. A. Vatutin

In this paper, we investigate the asymptotic behavior of continuous-state branching processes in a Brownian random environment (CBBRE) conditioned on non-extinction. For the subcritical case, we prove the existence of the Yaglom limit and…

Probability · Mathematics 2026-05-28 Pei-Sen Li , Xiangqi Zheng , Xiaowen Zhou

This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…

Probability · Mathematics 2011-10-28 Elena Dyakonova , Vladimir Vatutin , Serik Sagitov

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…

Probability · Mathematics 2023-02-07 M Peigné , C Pham

Branching Processes in Random Environment (BPREs) $(Z\_n:n\geq0)$ are the generalization of Galton-Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical regime, the…

Probability · Mathematics 2017-01-06 Vincent Bansaye , Christian Boeinghoff

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…

Probability · Mathematics 2019-04-01 Vladimir Vatutin , Elena Dyakonova

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…

Probability · Mathematics 2011-08-11 Valeriy Afanasyev , Christian Böinghoff , Götz Kersting , Vladimir Vatutin

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…

Probability · Mathematics 2018-12-27 V. A. Vatutin , E. E. Dyakonova

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…

Probability · Mathematics 2016-12-12 Vladimir A. Vatutin , Elena E. Dyakonova

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…

Probability · Mathematics 2017-09-13 Nina Gantert , Stefan Junk

In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed L\'{e}vy process $X$ in $\mathbb{R}$. Let $\zeta$ denote the extinction time, $M_t$ be the maximal…

Probability · Mathematics 2025-10-21 Yan-Xia Ren , Renming Song , Yaping Zhu

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…

Probability · Mathematics 2020-09-09 E. E. Dyakonova , V. A. Vatutin

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.

Probability · Mathematics 2022-08-08 E. E. Dyakonova

We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the…

Probability · Mathematics 2020-03-05 Pratima Hebbar , Leonid Koralov , James Nolen

We consider a particular Branching Random Walk in Random Environment (BRWRE) on $\sN_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which depends on the location) and move either one…

Probability · Mathematics 2009-12-01 Christian Bartsch , Nina Gantert , Michael Kochler
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