MULTITYPE BRANCHING PROCESSES IN RANDOM ENVIRONMENT: PROBABILITY OF SURVIVAL FOR THE CRITICAL CASE

V. A. Vatutin, E. E. Dyakonova

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

2 Цитирования (Scopus)

Аннотация

We investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in an environment generated by a sequence of independent identically distributed random variables. Under fairly general assumptions on the form of the offspring generating functions of particles, we show that the probability of survival up to generation n of the process initiated at moment. zero by a single particle of type i is equivalent to beta i(n-1/2), where beta(i) is a positive constant. This assertion essentially generalizes a number of previously known results.

Язык оригиналаанглийский
Страницы (с-по)506-521
Число страниц16
ЖурналTheory of Probability and its Applications
Том62
Номер выпуска4
DOI
СостояниеОпубликовано - 1 янв 2018

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