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 -