Sciact
  • EN
  • RU

The local principle of large deviations for compound poisson process with catastrophes Full article

Journal Brazilian Journal of Probability and Statistics
ISSN: 0103-0752
Output data Year: 2021, Volume: 35, Number: 2, Pages: 205-223 Pages count : 19 DOI: 10.1214/20-BJPS472
Tags Compound poisson processes; Large deviation principle; Local large deviation principle; Processes with catastrophes; Processes with resettings
Authors Logachov A. 1,2,3 , Logachova O. 3,4 , Yambartsev A. 5
Affiliations
1 Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Koptyuga str. 4, Novosibirsk, 630090, Russian Federation
2 Novosibirsk State University, Pirogova str. 1, Novosibirsk, 630090, Russian Federation
3 Novosibirsk State University of Economics and Management, Kamenskaya str. 56, Novosibirsk, 630099, Russian Federation
4 Siberian State University of Geo-systems and Technologies, Plakhotnogo str. 10, Novosibirsk, 630108, Russian Federation
5 Institute of Mathematics and Statistics, University of São Paulo, 1010 Rua do Matão, São Paulo SP, CEP 05508–090, Brazil

Funding (1)

1 Russian Science Foundation 18-11-00129

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. © Brazilian Statistical Association, 2021.
Cite: 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. V.35. N2. P.205-223. DOI: 10.1214/20-BJPS472 WOS Scopus OpenAlex
Identifiers:
Web of science: WOS:000632876700001
Scopus: 2-s2.0-85105304139
OpenAlex: W3154944629
Citing:
DB Citing
Scopus 2
OpenAlex 3
Web of science 2
Altmetrics: