Properties of multitype subcritical branching processes in random environment

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Properties of multitype subcritical branching processes in random environment. / Vatutin, Vladimir A.; Dyakonova, Elena E.

In: Discrete Mathematics and Applications, Vol. 31, No. 5, 01.10.2021, p. 367-382.

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

Harvard

Vatutin, VA & Dyakonova, EE 2021, 'Properties of multitype subcritical branching processes in random environment', Discrete Mathematics and Applications, vol. 31, no. 5, pp. 367-382. https://doi.org/10.1515/dma-2021-0032

APA

Vatutin, V. A., & Dyakonova, E. E. (2021). Properties of multitype subcritical branching processes in random environment. Discrete Mathematics and Applications, 31(5), 367-382. https://doi.org/10.1515/dma-2021-0032

Vancouver

Vatutin VA, Dyakonova EE. Properties of multitype subcritical branching processes in random environment. Discrete Mathematics and Applications. 2021 Oct 1;31(5):367-382. doi: 10.1515/dma-2021-0032

Author

Vatutin, Vladimir A. ; Dyakonova, Elena E. / Properties of multitype subcritical branching processes in random environment. In: Discrete Mathematics and Applications. 2021 ; Vol. 31, No. 5. pp. 367-382.

BibTeX

@article{95277fd77c0a4ba98d5c1b11dcc6c0c7,

title = "Properties of multitype subcritical branching processes in random environment",

abstract = "We study properties of a p-type subcritical branching process in random environment initiated at moment zero by a vector z = (z1,.., zp) of particles of different types. For p = 1 the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment n behaves as C(z)λn for large n, where the parameters λ ∈ (0, 1) and C(z) ∈ (0, ∞) are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment n → ∞ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process. ",

keywords = "limit theorems, multitype branching processes, random environment",

author = "Vatutin, {Vladimir A.} and Dyakonova, {Elena E.}",

note = "Funding Information: Funding : This work was supported by the Russian Science Foundation under the grant 17-11-01173. Publisher Copyright: {\textcopyright} 2021 Walter de Gruyter GmbH, Berlin/Boston.",

year = "2021",

month = oct,

day = "1",

doi = "10.1515/dma-2021-0032",

language = "English",

volume = "31",

pages = "367--382",

journal = "Discrete Mathematics and Applications",

issn = "0924-9265",

publisher = "Walter de Gruyter GmbH",

number = "5",

}

RIS

TY - JOUR

T1 - Properties of multitype subcritical branching processes in random environment

AU - Vatutin, Vladimir A.

AU - Dyakonova, Elena E.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We study properties of a p-type subcritical branching process in random environment initiated at moment zero by a vector z = (z1,.., zp) of particles of different types. For p = 1 the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment n behaves as C(z)λn for large n, where the parameters λ ∈ (0, 1) and C(z) ∈ (0, ∞) are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment n → ∞ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process.

AB - We study properties of a p-type subcritical branching process in random environment initiated at moment zero by a vector z = (z1,.., zp) of particles of different types. For p = 1 the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment n behaves as C(z)λn for large n, where the parameters λ ∈ (0, 1) and C(z) ∈ (0, ∞) are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment n → ∞ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process.

KW - limit theorems

KW - multitype branching processes

KW - random environment

UR - http://www.scopus.com/inward/record.url?scp=85117918654&partnerID=8YFLogxK

U2 - 10.1515/dma-2021-0032

DO - 10.1515/dma-2021-0032

M3 - Article

AN - SCOPUS:85117918654

VL - 31

SP - 367

EP - 382

JO - Discrete Mathematics and Applications

JF - Discrete Mathematics and Applications

SN - 0924-9265

IS - 5

ER -

ID: 34606204