Large deviations in a population dynamics with catastrophes

Author(s)

Logachov, A. ^{[1, 2, 3]} ; Logachova, O. ^{[3, 4]} ; Yambartsev, A. ^[5]

Affiliation

^[1] RAS, Sobolev Inst Math, Lab Probabil Theory & Math Stat, Siberian Branch, Koptyuga Str 4, Novosibirsk 630090 - Russia

^[2] Novosibirsk State Univ, Pirogova Str 1, Novosibirsk 630090 - Russia

^[3] Novosibirsk State Univ Econ & Management, Kamenskaya Str 56, Novosibirsk 630099 - Russia

^[4] Siberian State Univ Geosyst & Technol, Plakhotnogo Str 10, Novosibirsk 630108 - Russia

^[5] Univ Sao Paulo, Inst Math & Stat, 1010 Rua Matao, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Statistics & Probability Letters; v. 149, p. 29-37, JUN 2019.
• Web of Science Citations: 0

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. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 17/20482-0 - Large deviations principle for stochastic processes
• Grantee: Anatoli Iambartsev
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants