Research output: Contribution to conference › Abstract › peer-review
Branching process in random environment with immigration : life periods and survival of a single family. / Ватутин, Владимир Алексеевич; Дьяконова, Елена Евгеньевна.
2020. Abstract from Научная сессия МИАН, посвященная подведению итогов 2020 года, Москва, Russian Federation.Research output: Contribution to conference › Abstract › peer-review
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TY - CONF
T1 - Branching process in random environment with immigration
T2 - Научная сессия МИАН, посвященная подведению итогов 2020 года
AU - Ватутин, Владимир Алексеевич
AU - Дьяконова, Елена Евгеньевна
PY - 2020
Y1 - 2020
N2 - 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)→∞.
AB - 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)→∞.
UR - https://youtu.be/DNHt80td_-w
M3 - Abstract
Y2 - 25 November 2020 through 25 November 2020
ER -
ID: 27125786