带移民和瞬态拯救的二次加权分枝过程的相关性质  

The Properties of Quadratic Weighted Markov BranchingProcesses with Immigration and Instantaneous Resurrection

作　　者：孟维维 奚成勋 MENG Weiwei;XI Chengxun(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang,050043,China)

机构地区：[1]石家庄铁道大学数理系,石家庄050043

出　　处：《应用概率统计》2023年第5期711-729,共19页Chinese Journal of Applied Probability and Statistics

基　　金：河北省高等学校科学技术研究项目(批准号:QN2019085)资助。

摘　　要：本文考虑一类带有移民和瞬态拯救的二次加权分枝过程.在拯救速率可和的条件下,证明了目标过程不存在.研究拯救速率不可和的情形,得到了过程存在性判别准则与唯一性判别准则,并针对存在性给出了便于验证的等价条件.对于满足存在性条件的q矩阵Q,证明可以找出无穷多个Q过程,其中不中断Q过程却是唯一的.讨论了不中断Q过程的构造方式,证明了不中断Q过程是遍历的,且给出了平稳分布满足的二阶微分方程.We consider quadratic weighted branching processes with immigration and instantaneous res-urrection.Under the condition that the resurrection rate can be summed,we show that the target process does not exist.The existence and uniqueness criterion for the process are obtained under the assumption that the sum of the resurrection is infinite.Also,the equivalent conditions for the existence criterion are given for easy verification.It is proved that there exist infinitely many of Q processes.Among them,there exists a unique honest process and the corresponding construction method is then investigated.We prove that this honest process is always ergodic and the second-order differential equation of the equilibrium distribution is established.

关 键 词：二次加权 Markov分枝过程 瞬态拯救 常返性 遍历性 

分 类 号：O211.62[理学—概率论与数理统计]