The survival probability of a weakly subcritical multitype branching process in iid random environment

TL;DR

This paper analyzes the long-term survival chances of a multitype branching process in random environments, showing that the survival probability decreases at a specific polynomial-exponential rate under certain conditions.

Contribution

It provides a precise asymptotic formula for the survival probability of weakly subcritical multitype branching processes in iid environments, extending existing theory.

Findings

Survival probability decays as $ ho^n n^{-3/2}$ for some $ ho ext{ in } (0,1)$

Identifies conditions under which the asymptotic behavior holds

Enhances understanding of multitype branching processes in random environments

Abstract

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 some $\rho \in (0, 1)$ to specify.