生灭型半马氏骨架过程

The Birth and Death Type Semi-Markov Skeleton Process

本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τ__(n-1)(w)与τ_n(w)之间的嵌入过程X^((n))(t,w)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布.

In this paper,firstly,the definition of the birth and death type semi-Markov skeleton processes is introduced.The initial distribution and the life distribution of X^（（n））（t,ω） which imbed between skeleton sequence timesτ_（n-1）（ω） and T_n（ω） are obtained,the one-dimensional distribution of the birth and death type semi-Markov skeleton processes is derived.Secondly,the numerals characteristics of the birth and death type semi-Markov skeleton processes are introduced and their probability meanings and relationships are studied. Then we deal with the up and down integral type random functionals of the birth and death type semi-Markov skeleton processes.Thirdly,it＇s ergodicity and stationary distribution are discussed.The average times of first arrive time and recurrent time are obtained. The necessary and sufficient conditions of recurrent and positive recurrent are given,and it＇s stationary distribution is computed if it is positive recurrent.