Skip to main content

Research Repository

Advanced Search

Long term behaviour of two interacting birth-and-death processes

Menshikov, Mikhail; Shcherbakov, Vadim

Long term behaviour of two interacting birth-and-death processes Thumbnail


Authors

Vadim Shcherbakov



Abstract

In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates that are given by functions with suitable monotonicity properties. This is in line with the approach proposed by Gause and Kolmogorov for modelling interaction between species in ecology. We obtain conditions for transience/recurrence of the Markov chain and describe in detail its asymptotic behaviour in special transient cases.

Citation

Menshikov, M., & Shcherbakov, V. (2018). Long term behaviour of two interacting birth-and-death processes. Markov processes and related fields, 24(1), 85-106

Journal Article Type Article
Acceptance Date Apr 20, 2018
Publication Date May 1, 2018
Deposit Date May 3, 2018
Publicly Available Date Mar 28, 2024
Journal Markov processes and related fields.
Print ISSN 1024-2953
Publisher Polymat
Peer Reviewed Peer Reviewed
Volume 24
Issue 1
Pages 85-106
Publisher URL http://math-mprf.org/journal/articles/id1485/

Files




You might also like



Downloadable Citations