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

Menshikov, Mikhail; Shcherbakov, Vadim

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: May 3, 2018
• Journal: Markov processes and related fields.
• Print ISSN: 1024-2953
• Publisher: Polymat
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 1
• Pages: 85-106
• Public URL: https://durham-repository.worktribe.com/output/1327496
• Publisher URL: http://math-mprf.org/journal/articles/id1485/