Max-Compound Cox Processes. I
- Авторы: Korolev V.1,2,3, Sokolov I.2,1, Gorshenin A.2,1
-
Учреждения:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
- Hangzhou Dianzi University
- Выпуск: Том 237, № 6 (2019)
- Страницы: 789-803
- Раздел: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242454
- DOI: https://doi.org/10.1007/s10958-019-04205-0
- ID: 242454
Цитировать
Аннотация
Extreme values are considered in samples with random size that have a mixed Poisson distribution that is generated by a doubly stochastic Poisson process. Some inequalities are proved relating the distributions and moments of extrema with those of the leading process (the mixing distribution). Limit theorems are proved for the distributions of max-compound Cox processes, and limit distributions are described. An important particular case of the negative binomial distribution of a sample size corresponding to the case where the Cox process is led by a gamma Lévy process is considered, explaining a possible genesis of tempered asymptotic models.
Об авторах
V. Korolev
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Hangzhou Dianzi University
Автор, ответственный за переписку.
Email: vkorolev@cs.msu.ru
Россия, Moscow; Moscow; Hangzhou
I. Sokolov
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Email: vkorolev@cs.msu.ru
Россия, Moscow; Moscow
A. Gorshenin
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Email: vkorolev@cs.msu.ru
Россия, Moscow; Moscow