Linear competition processes and generalised Polya urns with removals. / Shcherbakov, Vadim; Volkov, Stanislav.

2020. (ArXiv.org).

Research output: Working paper

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Linear competition processes and generalised Polya urns with removals. / Shcherbakov, Vadim; Volkov, Stanislav.

2020. (ArXiv.org).

Research output: Working paper

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@techreport{17ebcd7299e2459f92fa66ae9b19e23c,
title = "Linear competition processes and generalised Polya urns with removals",
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 holds for the relevant generalized Polya urn model with removals.",
author = "Vadim Shcherbakov and Stanislav Volkov",
year = "2020",
month = jan,
day = "7",
language = "English",
series = "ArXiv.org",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Linear competition processes and generalised Polya urns with removals

AU - Shcherbakov, Vadim

AU - Volkov, Stanislav

PY - 2020/1/7

Y1 - 2020/1/7

N2 - 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 Polya urn model with removals.

AB - 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 Polya urn model with removals.

M3 - Working paper

T3 - ArXiv.org

BT - Linear competition processes and generalised Polya urns with removals

ER -