On the survival of a class of subcritical branching processes in random environment
type: Dataset
description: 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 that the density of $X$ has the form $$p_{X}(x)=x^{-\beta -1}l_{0}(x)e^{-\rho x}$$ for some $\beta >2,$ a slowly varying function $l_{0}(x)$ and $\rho \in \left( 0,1\right),$ we find the asymptotic survival probability and prove a Yaglom type conditional limit theorem for the process. The survival probability decreases exponentially with an additional polynomial term related to the tail of $X$. The proof relies on a fine study of a random walk (with negative drift and heavy tails) conditioned to stay positive until time $n$ and to have a small positive value at time $n$, with $n$ tending to infinity.
issued: 2026-05-07T17:50:05.740048
language: en
modified: 2026-05-07T17:50:05.740052
contact point: Organization
  fn: CCSD
keyword: 60j80-60k37-60j05
keyword: branching-processes
keyword: heavy-tails
keyword: infoeu-reposemanticsreport
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: random-environment
keyword: random-walk
keyword: reports
keyword: survival-probability
landing page: https://hal.science/hal-00844584

On the survival of a class of subcritical branching processes in random environment
type: Distribution
format: HTML
issued: 2026-05-07T17:50:05.742401
modified: 2026-05-07T17:50:05.729382
access URL: https://hal.science/hal-00844584

test_moissonnage_selune
type: Agent