A generating function approach to Markov chains undergoing binomial catastrophes

TL;DR

This paper uses generating functions to analyze Markov chain population models with binomial catastrophes, exploring the balance between growth via immigration and mass removal through catastrophic events.

Contribution

It introduces a generating function approach to study two variants of population models with binomial catastrophes, highlighting their subtle balance.

Findings

Describes the equilibrium between birth and death effects.

Analyzes two different stochastic models of catastrophes.

Provides insights into population dynamics under catastrophic events.

Abstract

In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a slightly different random nature. In both cases, we describe the subtle balance between the two birth and death conflicting effects.