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, random environment, survival probability, intermediately subcritical process, change of measures.
Citation:
V. A. Vatutin, E. E. D'yakonova, “The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment”, Mat. Zametki, 107:2 (2020), 163–177; Math. Notes, 107:2 (2020), 189–200
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\paper The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment
\jour Mat. Zametki
\yr 2020
\vol 107
\issue 2
\pages 163--177
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\jour Math. Notes
\yr 2020
\vol 107
\issue 2
\pages 189--200
\crossref{https://doi.org/10.1134/S0001434620010198}
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Linking options:
https://www.mathnet.ru/eng/mzm12395
https://doi.org/10.4213/mzm12395
https://www.mathnet.ru/eng/mzm/v107/i2/p163
This publication is cited in the following 7 articles:
M. Peigné, C. Pham, “The survival probability of a weakly subcritical multitype branching process in iid random environment”, Electron. J. Probab., 29:none (2024)
H. Wang, H. Liao, X. Ma, “Stochastic multi-phase modeling and health assessment for systems based on degradation branching processes”, Reliab. Eng. Syst. Saf., 222 (2022), 108412
I. Makarova, D. Balashova, S. Molchanov, E. Yarovaya, “Branching random walks with two types of particles on multidimensional lattices”, Mathematics, 10:6 (2022), 867
A. A. Imomov, A. Kh. Meiliev, “Ob asimptoticheskoi strukture nekriticheskikh markovskikh vetvyaschikhsya sluchainykh protsessov s nepreryvnym vremenem”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2021, no. 69, 22–36
V. A. Vatutin, E. E. Dyakonova, “Multitype branching processes in random environment”, Russian Math. Surveys, 76:6 (2021), 1019–1063
Sh. K. Formanov, Sh. Yu. Jurayev, “On transient phenomena in branching random processes with discrete time”, Lobachevskii J. Math., 42:12 (2021), 2777–2784
Yanqing Wang, Quansheng Liu, “Asymptotic Properties of a Supercritical Branching Process with Immigration in a Random Environment”, Stochastics and Quality Control, 36:2 (2021), 145
Citation in format AMSBIB
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