# Branching processes in random environment with sibling dependence

## TL;DR

This paper analyzes the long-term survival probability of a particle population with dependent reproduction influenced by a random environment and sibling relationships, providing insights into complex branching processes.

## Contribution

It introduces a model of branching processes in random environments incorporating sibling dependence and studies their asymptotic survival behavior.

## Key findings

- Derived asymptotic formulas for survival probabilities
- Identified conditions affecting population extinction or persistence
- Extended classical branching process theory to include sibling dependence

## Abstract

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 relatives of the particle. We study the asymptotic behavior of the survival probability of the population up to a distant moment n under some restrictions on the properties of the environment and family ties.