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

被引：0
作者：
V. A. Vatutin
E. E. D’yakonova
机构：
[1] Novosibirsk State University,
来源：
Mathematical Notes | 2020年 / 107卷
关键词：
branching process; random environment; survival probability; intermediately sub-critical process; change of measures;
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摘要：
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.
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页码：189 / 200
页数：11
相关论文
共 43 条
[1]  
Vatutin V A(1993)Branching processes. II J. Soviet Math. 67 3407-3485
[2]  
Zubkov A M(2018)A subcritical decomposable branching process in a mixed environment Diskret. Mat. 30 14-26
[3]  
D’yakonova E E(2018)Limit theorem for multi-type critical branching process evolving in a random environment Discrete Math. Appl. 28 275-283
[4]  
D’yakonova E E(2015)Multitype branching processes evolving in a Markovian environment Diskret. Mat. 27 44-58
[5]  
D’yakonova E E(2015)Multitype Galton—Watson branching processes in Markovian random environment Discrete Math. Appl. 25 137-147
[6]  
D’yakonova E E(2013)Asymptotic properties of multi-type critical branching processes evolving in a random environment Proc. Steklov Inst. Math. 282 80-89
[7]  
D’yakonova E E(2012)Critical multi-type branching processes in a random environment Diskret. Mat. 24 130-151
[8]  
D’yakonova E E(2012)The survival probability of a critical multi-type branching process in i.i.d. random environment Discrete Math. Appl. 22 639-664
[9]  
D’yakonova E E(2011)Multitype branching processes in random environment: Survival probability for the critical case Teor. Veroyatnost. Primenen. 56 592-601
[10]  
D’yakonova E E(2011)Multi-type subcritical branching processes in a random environment Theory Probab. Appl. 56 508-517
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