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2019 Metastability of a random walk with catastrophes
Luiz Renato Fontes, Rinaldo B. Schinazi
Electron. Commun. Probab. 24: 1-8 (2019). DOI: 10.1214/19-ECP275

Abstract

We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at $0$ for all parameter values. Recently, it has been shown that this chain exhibits a metastable behavior in the sense that it can persist for a very long time before getting absorbed. In this paper we study this metastable phase by making the parameters converge to extreme values. We obtain four different limits that we believe shed light on the metastable phase.

Citation

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Luiz Renato Fontes. Rinaldo B. Schinazi. "Metastability of a random walk with catastrophes." Electron. Commun. Probab. 24 1 - 8, 2019. https://doi.org/10.1214/19-ECP275

Information

Received: 2 July 2019; Accepted: 1 November 2019; Published: 2019
First available in Project Euclid: 9 November 2019

zbMATH: 07142641
MathSciNet: MR4029439
Digital Object Identifier: 10.1214/19-ECP275

Subjects:
Primary: 60J10, 60J80
Secondary: 60K37, 92D25

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