Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Thierry E. Huillet
Pages: [1] - [36]
Received Date: January 4, 2022
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100122243
In a Markov chain population model subject to catastrophes, random birth events, promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal. We study two versions of such population models when the binomial catastrophic events either comes from a fixed or random survival probability. In both cases, most of the time, the chain is ergodic and we are left with the description of its invariant equilibrium probability mass function. For such processes, the notion of discrete self-decomposability plays a key role in quantifying the degree of disaster of the equilibrium state.
Markov chain, random walk, random population growth, binomial catastrophe events, recurrence/transience transition, random survival probability, self-decomposability.
