一类上临界带移民分枝过程的下偏差估计  

Lower deviations for general supercritical branching process with immigration

作　　者：谢春艳 张梅[1] XIE Chunyan;ZHANG Mei(School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,100875,Beijing,China)

机构地区：[1]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875

出　　处：《北京师范大学学报（自然科学版）》2023年第1期1-8,共8页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(NSFC11871103);国家重点研发计划资助项目(2020YFA0712900)。

摘　　要：对于一类带移民的上临界分枝过程(Z_(n)),存在一列正常数c_(n)可以用来描述过程的增长速度.任取一列满足k_(n)→∞和k_(n)=o(c_(n))的正常数k_(n),P(Z_(n)=k_(n))的渐近行为即为Z_(n)的下偏差.假设EZ_(1)ln Z_(1)=∞:1)证明了过程Z_(n)的一个局部极限定理;2)给出了在Schröder和Böttcher情形下Z_(n)的下偏差估计,补充并完善了已有文献的结果.For a supercritical branching process with immigration(Z_(n)),a sequence of constant c_(n)could be used to describe the growth rate of the process.The asymptotic behavior of P(Z_(n)=k_(n))(k_(n)=o(c_(n)))is called the lower deviation probability of Z_(n).In this paper,under EZ_(1)ln Z_(1)=∞,first,a local limit theorem of Z_(n)is proved.Then in the Schröder and Böttcher cases,the lower deviation probability P(Z_(n)=k_(n))is discussed,which improves and generalizes the corresponding results in the literature.

关 键 词：上临界 带移民 分枝过程 下偏差 

分 类 号：O211.65[理学—概率论与数理统计]