单死过程的向下积分型泛函  

Integral-Type Functionals Downward of Single Death Processes

作　　者：王婧 张余辉[2] WANG Jing;ZHANG Yuhui(School of Mathematics and Statistics,Yili Normal University,Yili,835000,China;School of Mathematical Sciences,Beijing Normal University,Beijing,100875,China)

机构地区：[1]伊犁师范大学数学与统计学院,伊犁835000 [2]北京师范大学数学科学学院,北京100875

出　　处：《应用概率统计》2020年第4期393-414,共22页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11571043、11771047、11871008)资助。

摘　　要：本文对有限状态空间上单死过程,研究其向下积分型泛函的分布之Laplace变换和矩以及停留时间的分布.应用这些结果,给出可数状态空间上单死过程首中时高阶矩显式表示的一个新证明,同时,得到了强遍历收敛速率的上下界估计。In this paper we consider the integral-type functional downward of single death processes in the finite state space,including the Laplace transformation of its distribution and its polynomial moments as well as the distribution of staying times.As applications,a new proof for the recursive and explicit representation of high order moments of the first hitting times in the denumerable state space is presented;meanwhile,the estimates on the lower bound and the upper one of convergence rate in strong ergodicity are obtained.

关 键 词：单死过程 积分型泛函 首中时 停留时间 

分 类 号：O211.62[理学—概率论与数理统计]