Simulations and a conditional limit theorem for intermediately subcritical branching processes in random environment

TL;DR

This paper establishes a functional limit theorem for intermediately subcritical branching processes in random environments, highlighting their complex behavior at the critical borderline between two subcritical regimes, supported by simulations.

Contribution

It provides the first functional limit theorem for these processes and compares it with recent related theorems, deepening understanding of their asymptotic behavior.

Findings

Proves a new functional limit theorem for intermediately subcritical processes

Identifies complex behaviors at the critical subcritical boundary

Supports theoretical results with computer simulations

Abstract

Intermediately subcritical branching processes in random environment are at the borderline between two subcritical regimes and exhibit a particularly rich behavior. In this paper, we prove a functional limit theorem for these processes. It is discussed together with two other recently proved limit theorems for the intermediately subcritical case and illustrated by several computer simulations.