Standard

The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment. / Vatutin, V. A.; D’yakonova, E. E.

In: Mathematical Notes, Vol. 107, No. 1-2, 01.01.2020, p. 189-200.

Research output: Contribution to journal › Article › peer-review

Harvard

Vatutin, VA & D’yakonova, EE 2020, 'The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment', Mathematical Notes, vol. 107, no. 1-2, pp. 189-200. https://doi.org/10.1134/S0001434620010198

APA

Vatutin, V. A., & D’yakonova, E. E. (2020). The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment. Mathematical Notes, 107(1-2), 189-200. https://doi.org/10.1134/S0001434620010198

Vancouver

Vatutin VA, D’yakonova EE. The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment. Mathematical Notes. 2020 Jan 1;107(1-2):189-200. doi: 10.1134/S0001434620010198

Author

Vatutin, V. A. ; D’yakonova, E. E. / The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment. In: Mathematical Notes. 2020 ; Vol. 107, No. 1-2. pp. 189-200.

BibTeX

@article{4d5f5c6e8b164f52bacf59d83a976e4e,
title = "The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment",
abstract = "The asymptotic behavior of the survival probability for multi-type branching processes in a random environment is studied. In the case where all particles are of one type, the class of processes under consideration corresponds to intermediately subcritical processes. Under fairly general assumptions on the form of the generating functions of the laws of reproduction of particles, it is proved that the survival probability at a remote instant n of time for a process that started at the zero instant of time from one particle of any type is of the order of λnn−1/2, where λ ∈ (0, 1) is a constant defined in terms of the Lyapunov exponent for products of the mean-value matrices of the laws of reproduction of particles.",
keywords = "branching process, change of measures, intermediately sub-critical process, random environment, survival probability, LIMIT-THEOREMS, PRODUCTS",
author = "Vatutin, {V. A.} and D{\textquoteright}yakonova, {E. E.}",
year = "2020",
month = jan,
day = "1",
doi = "10.1134/S0001434620010198",
language = "English",
volume = "107",
pages = "189--200",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "PLEIADES PUBLISHING INC",
number = "1-2",

}

RIS

TY - JOUR

T1 - The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment

AU - Vatutin, V. A.

AU - D’yakonova, E. E.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The asymptotic behavior of the survival probability for multi-type branching processes in a random environment is studied. In the case where all particles are of one type, the class of processes under consideration corresponds to intermediately subcritical processes. Under fairly general assumptions on the form of the generating functions of the laws of reproduction of particles, it is proved that the survival probability at a remote instant n of time for a process that started at the zero instant of time from one particle of any type is of the order of λnn−1/2, where λ ∈ (0, 1) is a constant defined in terms of the Lyapunov exponent for products of the mean-value matrices of the laws of reproduction of particles.

AB - The asymptotic behavior of the survival probability for multi-type branching processes in a random environment is studied. In the case where all particles are of one type, the class of processes under consideration corresponds to intermediately subcritical processes. Under fairly general assumptions on the form of the generating functions of the laws of reproduction of particles, it is proved that the survival probability at a remote instant n of time for a process that started at the zero instant of time from one particle of any type is of the order of λnn−1/2, where λ ∈ (0, 1) is a constant defined in terms of the Lyapunov exponent for products of the mean-value matrices of the laws of reproduction of particles.

KW - branching process

KW - change of measures

KW - intermediately sub-critical process

KW - random environment

KW - survival probability

KW - LIMIT-THEOREMS

KW - PRODUCTS

UR - http://www.scopus.com/inward/record.url?scp=85080992261&partnerID=8YFLogxK

U2 - 10.1134/S0001434620010198

DO - 10.1134/S0001434620010198

M3 - Article

AN - SCOPUS:85080992261

VL - 107

SP - 189

EP - 200

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 23740607