Show Summary Details
More options …

# Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year

CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

Online
ISSN
1569-3929
See all formats and pricing
More options …
Volume 26, Issue 3

# Extinction of decomposable branching processes

/ Elena E. Dyakonova
Published Online: 2016-07-15 | DOI: https://doi.org/10.1515/dma-2016-0016

## Abstract

The asymptotic behavior, as n → ∞, of the conditional distribution of the number of particles in a decomposable critical branching process Z(m) = (Z1 (m), …, ZN(m)) with N types of particles at moment m = nk, k = 0(n), is investigated given that the extinction moment of the process equals to n.

Note: Originally published in Diskretnaya Matematika (2015) 27, ${\mathrm{N}}^{\underset{_}{o}}$4, 26–37 (in Russian).

## References

• [1]

Athreya K.B., Ney P.E., Branching Processes, Berlin: Springer, 1972.Google Scholar

• [2]

Kozlov M.V., “On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment”, Theory Probab. Appl., 21:4 (1977), 791–804.Google Scholar

• [3]

Afanasyev V.I., “Functional limit theorems for the decomposable branching process with two types of particles”, Discrete Math. Appl., 26 (2016), 71–88.

• [4]

Vatutin V.A., Dyakonova E.E., “Decomposable branching processses with a fixed moment of extinction”, Proc. Steklov Inst.Mathem., 290 (2015) (to appear).Google Scholar

• [5]

Foster J., Ney P., “Decomposable critical multi-type branching processes”, Sanhya: the Indian J. Statist., Ser. A, 38 (1976), 28–37.Google Scholar

• [6]

Foster J., Ney P., “Limit laws for decomposable critical branching processes”, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 46 (1978), 13–43.Google Scholar

• [7]

Markushevich A.I., The theory of analytic functions, Translated from the second Russian edition, Delhi: Hindustan Publishing Corp., 1963.Google Scholar

• [8]

Ogura Y., “Asymptotic behavior of multitype Galton-Watson processes”, J. Math. Kyoto Univ., 15 (1975), 251–302.Google Scholar

• [9]

Polin A. K., “Limit theorems for decomposable critical branching processes”, Mathematics of the USSR-Sbornik, 29:3 (1976), 377–392.Google Scholar

• [10]

Polin A. K., “Limit theorems for decomposable branching processes with final types”, Mathematics of the USSR-Sbornik, 33:1 (1977), 136–146.Google Scholar

• [11]

Savin A. A., Chistyakov V. P., “Some theorems for branching processes with several types of particles”, Theory Probab. Appl., 7:1 (1962), 93–100.Google Scholar

• [12]

Vatutin V. A., “The structure of decomposable reduced branching processes. I. Finite-dimensional distributions”, Theory Probab. Appl., 59:4 (2015), 641–662.Google Scholar

• [13]

Vatutin V. A., Sagitov S. M., “A decomposable critical branching process with two types of particles”, Proc. Steklov Inst. Math., 177 (1988), 1–19.Google Scholar

• [14]

Vatutin V.A., Dyakonova E.E., Jagers P., Sagitov S.M., “A decomposable branching process in a markovian environment”, Article ID 694285, Int. J. Stoch. Analysis, 2012 (2012), 24 pp.Google Scholar

• [15]

Zubkov A. M., “The limit behaviour of decomposable critical branching processes with two types of particles”, Theory Probab. Appl., 27:2 (1983), 235–237.Google Scholar

Published Online: 2016-07-15

Published in Print: 2016-07-01

Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-50-00005

This work was supported by the Russian Science Foundation under grant no. 14-50-00005

Citation Information: Discrete Mathematics and Applications, Volume 26, Issue 3, Pages 183–192, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265,

Export Citation

© 2016 Walter de Gruyter GmbH, Berlin/Boston.