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Random population dynamics under catastrophic events

Part of: Markov processes Difference and functional equations, recurrence relations Partial differential equations Stability theory

Published online by Cambridge University Press:  15 August 2022

Patrick Cattiaux ,
Jens Fischer ,
Sylvie Rœlly  and
Samuel Sindayigaya
Patrick Cattiaux*
Affiliation:
Université de Toulouse
Jens Fischer*
Affiliation:
Université de Toulouse and Universität Potsdam
Sylvie Rœlly*
Affiliation:
Universität Potsdam
Samuel Sindayigaya*
Affiliation:
Institut d’Enseignement Supérieur de Ruhengeri
*
*Postal address: Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX 9, France. Email address: patrick.cattiaux@math.univ-toulouse.fr
**Postal address: Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX 9, France; Institut für Mathematik der Universität Potsdam, Karl-Liebknecht-Str. 24–25, 14476 Potsdam OT Golm, Germany. Email address: jens.fischer@math.univ-toulouse.fr
***Postal address: Institut für Mathematik der Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam OT Golm, Germany. Email address: roelly@math.uni-potsdam.de
****Postal address: Institut d’Enseignement Supérieur de Ruhengeri, Musanze Street NM 155, PO Box 155, Ruhengeri, Rwanda. Email address: sindasam12@gmail.com
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Abstract

In this paper we introduce new birth-and-death processes with partial catastrophe and study some of their properties. In particular, we obtain some estimates for the mean catastrophe time, and the first and second moments of the distribution of the process at a fixed time t. This is completed by some asymptotic results.

Keywords

Birth-and-death processpopulation dynamicsextinction timebirthdeathand catastrophe process

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 65Q30: Recurrence relations 34D45: Attractors 35B40: Asymptotic behavior of solutions
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 4 , December 2022 , pp. 962 - 982
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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