Boundary effect in compretition processes
(2019) In Journal of Applied Probability- Abstract
- This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent linear birth processes with immigration. Interactions of interest include, as a special case, the famous Lotka-Volterra interaction. The Markov chain with another special case of interaction can be interpreted as an urn model with ball removals and is reminiscent, in a sense, of Friedman's urn model. We show that, with probability one, eventually one of the components of the process tends to infinity, while the other component oscillates between values 0 and 1 (between values 0 and 2 in... (More)
- This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent linear birth processes with immigration. Interactions of interest include, as a special case, the famous Lotka-Volterra interaction. The Markov chain with another special case of interaction can be interpreted as an urn model with ball removals and is reminiscent, in a sense, of Friedman's urn model. We show that, with probability one, eventually one of the components of the process tends to infinity, while the other component oscillates between values 0 and 1 (between values 0 and 2 in a special case).
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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/93cc5174-3319-468a-a3a9-158ba13c4033
- author
- Shcherbakov, Vadim
and Volkov, Stanislav
LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Applied Probability
- publisher
- Applied Probability Trust
- ISSN
- 1475-6072
- language
- English
- LU publication?
- yes
- id
- 93cc5174-3319-468a-a3a9-158ba13c4033
- date added to LUP
- 2019-05-07 09:13:58
- date last changed
- 2021-04-16 10:29:35
@article{93cc5174-3319-468a-a3a9-158ba13c4033, abstract = {{This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent linear birth processes with immigration. Interactions of interest include, as a special case, the famous Lotka-Volterra interaction. The Markov chain with another special case of interaction can be interpreted as an urn model with ball removals and is reminiscent, in a sense, of Friedman's urn model. We show that, with probability one, eventually one of the components of the process tends to infinity, while the other component oscillates between values 0 and 1 (between values 0 and 2 in a special case).<br/>}}, author = {{Shcherbakov, Vadim and Volkov, Stanislav}}, issn = {{1475-6072}}, language = {{eng}}, publisher = {{Applied Probability Trust}}, series = {{Journal of Applied Probability}}, title = {{Boundary effect in compretition processes}}, year = {{2019}}, }