Generalized Markov interacting branching processes

被引：0

作者：

Junping Li ^{[1
]}

Anyue Chen ^{[2
,3
]}

机构：

[1] School of Mathematics and Statistics, Central South University

[2] Department of Mathematics, Southern University of Science and Technology

[3] Department of Mathematical Sciences, The University of Liverpool

来源：

Science China Mathematics | 2018年 / 61卷 / 03期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

generalized Markov interacting branching process; regularity; extinction probability; mean extinction time; mean explosive time; total mean life time;

D O I：

暂无

中图分类号：

O211.65 [分支过程];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.

引用

页码：545 / 562

页数：18

共 50 条

[41] A NOTE ON LIMIT THEOREMS FOR MARKOV BRANCHING PROCESSES
CONNER, H
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 18 (01) : 76 - &
[42] ON 2 DIMENSIONAL MARKOV PROCESSES WITH BRANCHING PROPERTY
WATANABE, S
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 136 (FEB) : 447 - &
[43] A remark on the uniqueness of weighted Markov branching processes
Chen, Anyue
Pollett, Phil
Li, Junping
Zhang, Hanjun
[J]. JOURNAL OF APPLIED PROBABILITY, 2007, 44 (01) : 279 - 283
[44] BRANCHING-PROCESSES AS MARKOV-FIELDS
JAGERS, P
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1987, 26 (02) : 189 - 189
[45] Extinction and explosion of nonlinear Markov branching processes
Pakes, Anthony G.
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 82 : 403 - 428
[46] Measure-valued branching Markov processes
Pap, Gyula
[J]. ACTA SCIENTIARUM MATHEMATICARUM, 2011, 77 (3-4): : 727 - 728
[47] RECURRENCE OF MARKOV BRANCHING-PROCESSES WITH IMMIGRATION
CHEN, A
RENSHAW, E
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 45 (02) : 231 - 242
[48] POISSON REPRESENTATIONS OF BRANCHING MARKOV AND MEASURE-VALUED BRANCHING PROCESSES
Kurtz, Thomas G.
Rodrigues, Eliane R.
[J]. ANNALS OF PROBABILITY, 2011, 39 (03): : 939 - 984
[49] The Properties of Generalized Collision Branching Processes
Wang, Juan
Cai, Chunhao
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020
[50] Multiquantum markov semigroups, interacting branching processes and nonlinear kinetic equations. Finite dimensional case.
Belavkin, VP
Williams, CR
[J]. QUANTUM PROBABILITY AND INFINITE DIMENSIONAL ANALYSIS, 2005, 18 : 67 - 104

← 1 2 3 4 5 →