# Branching processes in correlated random environment

## TL;DR

This paper investigates the survival probabilities and tail behaviors of critical branching processes in correlated random environments, especially those modeled by fractional Brownian motion, revealing new insights into their probabilistic properties.

## Contribution

It introduces analysis of critical branching processes in correlated environments, including fractional Brownian motion, providing new estimates for survival probabilities and tail distributions.

## Key findings

- Survival probability estimates for processes in correlated environments.
- Tail behavior of progeny and width in fractional Brownian motion environments.
- Extension of classical branching process results to correlated settings.

## Abstract

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 motion, we estimate also the tail of progeny as well as the tail of width.