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

Research output: Working paper

Submitted

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

Research output: Working paper

Shcherbakov, V & Volkov, S 2020 'Linear competition processes and generalised Polya urns with removals' ArXiv.org. <https://arxiv.org/abs/2001.01480>

Shcherbakov, V., & Volkov, S. (2020). *Linear competition processes and generalised Polya urns with removals*. (ArXiv.org). https://arxiv.org/abs/2001.01480

Shcherbakov V, Volkov S. Linear competition processes and generalised Polya urns with removals. 2020 Jan 7. (ArXiv.org).

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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",

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T1 - Linear competition processes and generalised Polya urns with removals

AU - Shcherbakov, Vadim

AU - Volkov, Stanislav

PY - 2020/1/7

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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

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BT - Linear competition processes and generalised Polya urns with removals

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