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The local principle of large deviations for compound poisson process with catastrophes. / Logachov, Artem; Logachova, Olga; Yambartsev, Anatoly.

In: Brazilian Journal of Probability and Statistics, Vol. 35, No. 2, 2021, p. 205-223.

Research output: Contribution to journal › Article › peer-review

Harvard

Logachov, A, Logachova, O & Yambartsev, A 2021, 'The local principle of large deviations for compound poisson process with catastrophes', Brazilian Journal of Probability and Statistics, vol. 35, no. 2, pp. 205-223. https://doi.org/10.1214/20-BJPS472

APA

Logachov, A., Logachova, O., & Yambartsev, A. (2021). The local principle of large deviations for compound poisson process with catastrophes. Brazilian Journal of Probability and Statistics, 35(2), 205-223. https://doi.org/10.1214/20-BJPS472

Vancouver

Logachov A, Logachova O, Yambartsev A. The local principle of large deviations for compound poisson process with catastrophes. Brazilian Journal of Probability and Statistics. 2021;35(2):205-223. doi: 10.1214/20-BJPS472

Author

Logachov, Artem ; Logachova, Olga ; Yambartsev, Anatoly. / The local principle of large deviations for compound poisson process with catastrophes. In: Brazilian Journal of Probability and Statistics. 2021 ; Vol. 35, No. 2. pp. 205-223.

BibTeX

@article{3970ac9eb99746eba30ac40a8bb81191,
title = "The local principle of large deviations for compound poisson process with catastrophes",
abstract = "The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle.",
keywords = "Compound poisson processes, Large deviation principle, Local large deviation principle, Processes with catastrophes, Processes with resettings",
author = "Artem Logachov and Olga Logachova and Anatoly Yambartsev",
note = "Funding Information: AL supported by RSF project 18-11-00129. AL thanks the Institute of Mathematics and Statistics of University of S{\~a}o Paulo for hospitality. AY also thanks CNPq and FAPESP for the financial support via the grants 301050/2016-3 and 2017/10555-0, respectively. Funding Information: This work is supported by FAPESP grant 2017/20482-0. Publisher Copyright: {\textcopyright} Brazilian Statistical Association, 2021.",
year = "2021",
doi = "10.1214/20-BJPS472",
language = "English",
volume = "35",
pages = "205--223",
journal = "Brazilian Journal of Probability and Statistics",
issn = "0103-0752",
publisher = "Associacao Brasileira de Estatistica",
number = "2",

}

RIS

TY - JOUR

T1 - The local principle of large deviations for compound poisson process with catastrophes

AU - Logachov, Artem

AU - Logachova, Olga

AU - Yambartsev, Anatoly

N1 - Funding Information: AL supported by RSF project 18-11-00129. AL thanks the Institute of Mathematics and Statistics of University of São Paulo for hospitality. AY also thanks CNPq and FAPESP for the financial support via the grants 301050/2016-3 and 2017/10555-0, respectively. Funding Information: This work is supported by FAPESP grant 2017/20482-0. Publisher Copyright: © Brazilian Statistical Association, 2021.

PY - 2021

Y1 - 2021

N2 - The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle.

AB - The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle.

KW - Compound poisson processes

KW - Large deviation principle

KW - Local large deviation principle

KW - Processes with catastrophes

KW - Processes with resettings

UR - http://www.scopus.com/inward/record.url?scp=85105304139&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46042431

U2 - 10.1214/20-BJPS472

DO - 10.1214/20-BJPS472

M3 - Article

AN - SCOPUS:85105304139

VL - 35

SP - 205

EP - 223

JO - Brazilian Journal of Probability and Statistics

JF - Brazilian Journal of Probability and Statistics

SN - 0103-0752

IS - 2

ER -

ID: 34144558