Processes with catastrophes: Large deviation point of view Full article
| Journal |
Stochastic Processes and their Applications
ISSN: 0304-4149 |
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| Output data | Year: 2024, Volume: 176, Article number : 104447, Pages count : 19 DOI: 10.1016/j.spa.2024.104447 | ||||||||
| Tags | Markov process, Stochastic processes with catastrophes, Law of large numbers, Large deviation principle, Rate function | ||||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
In this paper, we propose a new definition of catastrophes and present our results on large deviations for Poisson processes with catastrophes that satisfy this definition. Our earlier work focused on (almost) uniformly distributed catastrophes, but the current paper extends the results to a larger class of catastrophes. We show that the rate function remains the same regardless of the distribution of catastrophic events. Additionally, we extend and generalize our previous results on the limiting behavior of the supremum of the considered processes.
Cite:
Logachov A.
, Logachova O.
, Yambartsev A.
Processes with catastrophes: Large deviation point of view
Stochastic Processes and their Applications. 2024. V.176. 104447 :1-19. DOI: 10.1016/j.spa.2024.104447 WOS Scopus РИНЦ OpenAlex
Processes with catastrophes: Large deviation point of view
Stochastic Processes and their Applications. 2024. V.176. 104447 :1-19. DOI: 10.1016/j.spa.2024.104447 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 2, 2023 |
| Accepted: | Jul 23, 2024 |
| Published print: | Jul 29, 2024 |
| Published online: | Aug 1, 2024 |
Identifiers:
| Web of science: | WOS:001287528300001 |
| Scopus: | 2-s2.0-85200134709 |
| Elibrary: | 74048611 |
| OpenAlex: | W4401074572 |