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Multitype branching processes in random environment: probability of survaval for the critical case. / Vatutin, V. A.; Dyakonova, E. E.

в: Theory of Probability and its Applications, Том 62, № 4, 1, 01.01.2018, стр. 506-521.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Vatutin, VA & Dyakonova, EE 2018, 'Multitype branching processes in random environment: probability of survaval for the critical case', Theory of Probability and its Applications, Том. 62, № 4, 1, стр. 506-521. https://doi.org/10.1137/S0040585X97T988782

APA

Vatutin, V. A., & Dyakonova, E. E. (2018). Multitype branching processes in random environment: probability of survaval for the critical case. Theory of Probability and its Applications, 62(4), 506-521. [1]. https://doi.org/10.1137/S0040585X97T988782

Vancouver

Vatutin VA, Dyakonova EE. Multitype branching processes in random environment: probability of survaval for the critical case. Theory of Probability and its Applications. 2018 янв. 1;62(4):506-521. 1. doi: 10.1137/S0040585X97T988782

Author

Vatutin, V. A. ; Dyakonova, E. E. / Multitype branching processes in random environment: probability of survaval for the critical case. в: Theory of Probability and its Applications. 2018 ; Том 62, № 4. стр. 506-521.

BibTeX

@article{5e993972f0784335b22a30a6bac7323f,
title = "Multitype branching processes in random environment: probability of survaval for the critical case",
abstract = "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.",
keywords = "branching processes, random environment, survival probability, change of measure, LIMIT-THEOREMS, PRODUCTS, Random environment, Survival probability, Branching processes, Change of measure",
author = "Vatutin, {V. A.} and Dyakonova, {E. E.}",
note = "This research was supported by the Russian Science Foundation (project no. 17-11-01173). Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 62 (2017), pp. 634–653. http://www.siam.org/journals/tvp/62-4/T98878.html †Steklov Mathematical Institute of Russian Academy of Sciences, 119991 Moscow, Russia (vatutin@mi.ras.ru, elena@mi.ras.ru).",
year = "2018",
month = jan,
day = "1",
doi = "10.1137/S0040585X97T988782",
language = "English",
volume = "62",
pages = "506--521",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "SIAM PUBLICATIONS",
number = "4",

}

RIS

TY - JOUR

T1 - Multitype branching processes in random environment: probability of survaval for the critical case

AU - Vatutin, V. A.

AU - Dyakonova, E. E.

N1 - This research was supported by the Russian Science Foundation (project no. 17-11-01173). Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 62 (2017), pp. 634–653. http://www.siam.org/journals/tvp/62-4/T98878.html †Steklov Mathematical Institute of Russian Academy of Sciences, 119991 Moscow, Russia (vatutin@mi.ras.ru, elena@mi.ras.ru).

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - branching processes

KW - random environment

KW - survival probability

KW - change of measure

KW - LIMIT-THEOREMS

KW - PRODUCTS

KW - Random environment

KW - Survival probability

KW - Branching processes

KW - Change of measure

UR - http://www.scopus.com/inward/record.url?scp=85055210992&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=38644743

U2 - 10.1137/S0040585X97T988782

DO - 10.1137/S0040585X97T988782

M3 - Article

VL - 62

SP - 506

EP - 521

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 4

M1 - 1

ER -

ID: 18648897