Limit theorems for supercritical MBPRE with linear fractional offspring distributions

TL;DR

This paper studies the long-term behavior of supercritical multitype branching processes with linear fractional offspring distributions in random environments, revealing phase transitions and deriving conditional limit theorems.

Contribution

It introduces new limit theorems for supercritical multitype branching processes with linear fractional offspring distributions in random environments, highlighting phase transitions.

Findings

Existence of phase transition in local probabilities

Conditional limit theorems derived from generating functions

Identification of strongly and intermediately supercritical regimes

Abstract

We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of the process affected by strongly and intermediately supercritical regimes. Some conditional limit theorems can also be obtained from the representation of generating functions.