带移民的广义马尔可夫分支过程  

Generalized Markov Interacting Branching Processes with Immigration

作　　者：张培培 王娟 Zhang Peipei;Wang Juan(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《数学理论与应用》2019年第1期62-82,共21页Mathematical Theory and Applications

摘　　要：本文主要讨论带有移民的相互作用的广义马科夫分支过程的一些基本性质,该过程是对一般马科夫分支过程的自然推广.在得到一些关键的初步结果之后,我们给出一些关于过程正则性和唯一性的充分条件.然后很容易地计算出灭绝向量,并给出平均灭绝时间和条件平均灭绝时间的表达式,最后还研究和求解过程的平均爆炸时间和总平均寿命.This paper focuses on discussing some basic properties of the Markov interacting branching processes with immigration which is a natural generalization of the ordinary Markov branching process.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 the processes are also investigated and resolved.

关 键 词：分支过程 移民 正则性和唯一性 灭绝概率 平均灭绝时间 平均爆炸时间 

分 类 号：G63[文化科学—教育学]