Linear competition processes and generalized Pólya urns with removals
Popov, Serguei ; Shcherbakov, Vadim and Volkov, Stanislav LU
(2022)
In Stochastic Processes and their Applications
144.
p.125-152
- Abstract
A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also... (More)
A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Pólya urn model with removals.
(Less)
- author
- Popov, Serguei
; Shcherbakov, Vadim
and Volkov, Stanislav
LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Birth-and-death process, Branching process, Competition process, Generalized Pólya urn with removals, Martingale
- in
- Stochastic Processes and their Applications
- volume
- 144
- pages
- 28 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85119610763
- ISSN
- 0304-4149
- DOI
- 10.1016/j.spa.2021.11.001
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2021 Elsevier B.V.
- id
- b3c42314-70ae-461b-9e2c-9ba277545e9f
- date added to LUP
- 2021-12-02 14:16:51
- date last changed
- 2022-04-19 18:22:55
@article{b3c42314-70ae-461b-9e2c-9ba277545e9f,
abstract = {{<p>A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Pólya urn model with removals.</p>}},
author = {{Popov, Serguei and Shcherbakov, Vadim and Volkov, Stanislav}},
issn = {{0304-4149}},
keywords = {{Birth-and-death process; Branching process; Competition process; Generalized Pólya urn with removals; Martingale}},
language = {{eng}},
pages = {{125--152}},
publisher = {{Elsevier}},
series = {{Stochastic Processes and their Applications}},
title = {{Linear competition processes and generalized Pólya urns with removals}},
url = {{http://dx.doi.org/10.1016/j.spa.2021.11.001}},
doi = {{10.1016/j.spa.2021.11.001}},
volume = {{144}},
year = {{2022}},
}