Large deviations in a population dynamics with catastrophes

A. Logachov; O. Logachova; A. Yambartsev

doi:10.1016/j.spl.2019.01.029

Large deviations in a population dynamics with catastrophes

A. Logachov, O. Logachova, A. Yambartsev

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5 Citations (Scopus)

Abstract

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The large deviation result provides an optimal trajectory of large fluctuation: it shows how the large fluctuations occur for this class of processes.

Original language	English
Pages (from-to)	29-37
Number of pages	9
Journal	Statistics and Probability Letters
Volume	149
DOIs	https://doi.org/10.1016/j.spl.2019.01.029
Publication status	Published - 1 Jun 2019

Keywords

Catastrophes
Large deviation principle
Local large deviation principle
Population models

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10.1016/j.spl.2019.01.029

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abstract = "The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The large deviation result provides an optimal trajectory of large fluctuation: it shows how the large fluctuations occur for this class of processes.",

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AU - Logachova, O.

AU - Yambartsev, A.

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AB - The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The large deviation result provides an optimal trajectory of large fluctuation: it shows how the large fluctuations occur for this class of processes.

KW - Catastrophes

KW - Large deviation principle

KW - Local large deviation principle

KW - Population models

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DO - 10.1016/j.spl.2019.01.029

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SP - 29

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

Large deviations in a population dynamics with catastrophes

Abstract

Keywords

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