POISSON RANDOM MEASURES AND NONCRITICAL MULTITYPE MARKOV BRANCHING PROCESSES

被引：0

作者：

Slavtchova-Bojkova, Maroussia N. ^{[1
,3
]}

Hyrien, Ollivier ^{[2
]}

Yanev, Nikolay M. ^{[1
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Akad G Bonchev St,Bl 8, Sofia 1113, Bulgaria

[2] Fred Hutchinson Canc Res Ctr, Seattle, WA 98109 USA

[3] Sofia Univ St Kliment Ohridski, Fac Math & Informat, 5 J Bourchier Blvd, Sofia 1164, Bulgaria

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2021年 / 74卷 / 05期

关键词：

multitype Markov branching processes; immigration; Poisson measures; limiting distributions;

D O I：

10.7546/CRABS.2021.05.03

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We investigate noncritical multi-type Markov branching processes with immigration generated by Poisson measures. Limiting distributions are obtained when the rates of the Poisson measures are asymptotically equivalent to exponential or regularly varying functions. In particular, results analogous to a strong LLN are presented, and limiting normal distributions are obtained when the rates increase. When the rates decrease, then conditional limiting distributions are established. A stationary limiting distribution is obtained when the mean Poisson measure grows linearly. The asymptotic behaviour of the first and second moments of the processes is also investigated.

引用

页码：658 / 668

页数：11

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