|
ИСТИНА |
Войти в систему Регистрация |
ФНКЦ РР |
||
Complete classification of catalytic branching processesстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 16 февраля 2016 г.
- Автор: Bulinskaya E.Vl
- Журнал: Theory of Probability and its Applications
- Том: 59
- Номер: 4
- Год издания: 2015
- Издательство: Society for Industrial and Applied Mathematics
- Местоположение издательства: United States
- Первая страница: 545
- Последняя страница: 566
- DOI: 10.1137/S0040585X97T987314
- Аннотация: We study a catalytic branching process (CBP) with any finite set of catalysts. This model describes a system of particles where motion is governed by a Markov chain with finite or countable state space and the branching may only occur at the points of catalysis. The results obtained generalize and strengthen assertions known earlier in cases of CBP with a single catalyst and of branching random walk on ${\bf Z}^d$, $d\in{\bf N}$, with a finite number of sources of particles generation. We propose to classify CBP with $N$ catalysts as supercritical, critical, or subcritical according to the value of the Perron root of an $N\times N$ matrix. Such classification agrees with the moment analysis performed here for local and total particles numbers. The proofs of the main results are based on construction of auxiliary multitype Bellman--Harris processes with aid of the Markov chain hitting times of a catalyst position under taboo on visiting other catalysis points and on application of multidimensional renewal theorems.
- Добавил в систему: Булинская Екатерина Владимировна
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | Bulinskaya_2015_final.pdf | 256,9 КБ | 10 декабря 2015 [bulinskaya] |