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Population dynamics driven by truncated stable processes with Markovian switching

Part of: Markov processes Mathematical economics Mathematical biology in general Stochastic processes

Published online by Cambridge University Press:  23 June 2021

Zhenzhong Zhang ,
Jinying Tong ,
Qingting Meng  and
You Liang
Zhenzhong Zhang*
Affiliation:
Donghua University
Jinying Tong*
Affiliation:
Donghua University
Qingting Meng*
Affiliation:
Donghua University
You Liang*
Affiliation:
Ryerson University
*
**Email address: zzzhang@dhu.edu.cn
**Email address: zzzhang@dhu.edu.cn
**Email address: zzzhang@dhu.edu.cn
*Postal address: College of Science, Donghua University, 2999 People’s Road, Songjiang, Shanghai, 201620, China.
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Abstract

We focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.

Keywords

Ergodicityα-stable processesMarkovian switchingstationary distributionextinction

MSC classification

Primary: 60G52: Stable processes 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92B05: General biology and biomathematics 91B70: Stochastic models
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 2 , June 2021 , pp. 505 - 522
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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