一类上临界带移民分支过程的下偏差概率估计  

Lower Deviations for Supercritical Branching Processes with Immigration Concerning a Special Case

作　　者：孙琪 张梅[2] SUN Qi;ZHANG Mei(School of Mathematics and Statistics,Beijing Technology and Business University,Beijing,100048,China;School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems,Beijing Normal University,Beijing,100875,China)

机构地区：[1]北京工商大学数学与统计学院,北京100048 [2]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：《应用概率统计》2023年第6期879-896,共18页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11871103、12271043);国家重点研发计划项目(批准号:2020YFA0712-900);北京工商大学学科建设经费(批准号:STKY202305)资助.

摘　　要：对于后代分布为{pi,i≥0}的上临界带移民分支过程{Zn},如果分支和移民分布满足适当的矩条件,则Zn/m^(n)几乎处处收敛到某个非退化的极限,其中m:=∑_(i=0)^(∞)ipi为过程后代分布的均值.本文给出了p0>0时该过程下偏差概率P(Zn=k)的渐近行为,其中k∈[k_(n),m^(n)],k_(n)→∞(n→∞),这一结果可作为文献[8]中Schroder情形结论的补充.For a supercritical branching processes with immigration {Zn} with offspring distribution {pi,i≥0},it is known that under suitable conditions on the offspring and immigration distributions,Zn=mn converges almost surely to a finite and strictly positive limit,where m is the offspring mean.In certain situation p_(0)>0,we study the limiting properties of the probabilities P(Zn=k)with k∈[k_(n),m^(n)],k_(n)→∞(n→∞).Detailed asymptotic behavior of such lower deviation probabilities is given as a complement to our previous work[8].

关 键 词：上临界 分支过程 下偏差 移民 

分 类 号：O211.65[理学—概率论与数理统计] O211.4[理学—数学]