Markovian Arrival Process Subject to Renewal Generated Binomial Catastrophes

Kumar, Nitin; Gupta, Umesh C.

doi:10.1007/s11009-022-09929-2

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“…They are part of the q-series theory (see [4]). Further instances and applications of geometric catastrophes are detailed in [1,9,10,15,17], while examples and applications of binomial catastrophes can be found in [1,5,6,14,16,18].…”

Section: Introductionmentioning

confidence: 99%

Extinction time in growth models subject to binomial catastrophes ^*

Duque,

Junior,

Machado

et al. 2023

J. Stat. Mech.

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Populations are often subject to catastrophes that lead to significant reductions in the number of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the reported results, it has been considered whether dispersion strategies, at times of catastrophes, increase the survival probability of the population. In this paper, we contrast dispersion strategies by comparing the mean extinction times of a population under conditions of near-certain extinction. Specifically, we consider populations subject to binomial catastrophes, where the population size is reduced according to a binomial law when a catastrophe occurs. Our findings delineate the optimal strategy (dispersion or non-dispersion) based on variations in model parameter values.

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