Branching process in random environment with immigration: life periods and survival of a single family

Владимир Алексеевич Ватутин, Елена Евгеньевна Дьяконова

Research output: Contribution to conferenceAbstractpeer-review

Abstract

We consider branching processes with immigration evolving in an i.i.d. random environment.
Assuming that immigration is not allowed when there are no individuals in the population we investigate in [1, 2] the tail distribution of the so-called life period of the subcritical and critical processes, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.
We also investigate in [3] a branching process with immigration an i.i.d. random environment, in which one immigrant arrives at each generation. Let Ai(n) be the event that all individuals alive at time n are descendants of the immigrant which joined the population at time i. Assuming that the process is subcritical we investigate, as n→∞ the asymptotic behavior of the probability of the event Ai(n) when i is either fixed, or the difference n−i is fixed, or min(i,n−i)→∞.
Translated title of the contributionВетвящиеся процессы в случайной среде с иммиграцией: периоды жизни и выживание одного семейства
Original languageEnglish
Publication statusPublished - 2020
EventНаучная сессия МИАН, посвященная подведению итогов 2020 года - Онлайн, Москва, Russian Federation
Duration: 25 Nov 202025 Nov 2020

Workshop

WorkshopНаучная сессия МИАН, посвященная подведению итогов 2020 года
CountryRussian Federation
CityМосква
Period25.11.202025.11.2020

Fingerprint

Dive into the research topics of 'Branching process in random environment with immigration: life periods and survival of a single family'. Together they form a unique fingerprint.

Cite this