Boundary effect in competition processes
Shcherbakov, Vadim and Volkov, Stanislav LU
(2019)
In Journal of Applied Probability
56(3).
p.750-768
- Abstract
This paper is devoted to studying the long-term behaviour of a continuous-time Markov chain that can be interpreted as a pair of linear birth processes which evolve with a competitive interaction; as a special case, they include the famous Lotka-Volterra interaction. Another example of our process is related to urn models with ball removal. We show that, with probability one, the process eventually escapes to infinity by sticking to the boundary in a rather unusual way.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/582afc7a-2b05-4a74-bf26-c482a54417cb
- author
- Shcherbakov, Vadim
and Volkov, Stanislav
LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- birth-and-death process, competition process, Friedman's urn model, Lyapunov function, Markov chain, martingale
- in
- Journal of Applied Probability
- volume
- 56
- issue
- 3
- pages
- 19 pages
- publisher
- Applied Probability Trust
- external identifiers
-
- scopus:85072828515
- ISSN
- 0021-9002
- DOI
- 10.1017/jpr.2019.46
- language
- English
- LU publication?
- yes
- id
- 582afc7a-2b05-4a74-bf26-c482a54417cb
- date added to LUP
- 2019-10-17 10:56:49
- date last changed
- 2022-04-02 22:22:22
@article{582afc7a-2b05-4a74-bf26-c482a54417cb,
abstract = {{<p>This paper is devoted to studying the long-term behaviour of a continuous-time Markov chain that can be interpreted as a pair of linear birth processes which evolve with a competitive interaction; as a special case, they include the famous Lotka-Volterra interaction. Another example of our process is related to urn models with ball removal. We show that, with probability one, the process eventually escapes to infinity by sticking to the boundary in a rather unusual way.</p>}},
author = {{Shcherbakov, Vadim and Volkov, Stanislav}},
issn = {{0021-9002}},
keywords = {{birth-and-death process; competition process; Friedman's urn model; Lyapunov function; Markov chain; martingale}},
language = {{eng}},
number = {{3}},
pages = {{750--768}},
publisher = {{Applied Probability Trust}},
series = {{Journal of Applied Probability}},
title = {{Boundary effect in competition processes}},
url = {{http://dx.doi.org/10.1017/jpr.2019.46}},
doi = {{10.1017/jpr.2019.46}},
volume = {{56}},
year = {{2019}},
}