非齐次可列马尔可夫过程的轨道性质

§1 状态分类 定义1.1 设I是非负整数集,P={P_(ij)(s,t)|i,j∈I,α≤s≤t≤b}是转移函数矩阵。称P对i在t右标准,若limp_(ii)(t,t+h)=1;称P对i在t左标准,若limP_(ii)(t-h,t)=1.若P对i在t同时为右标准的和左标准的,则称P对i在t标准。若P对i在每个t标准,则称P对i标准。P对i右标准或左标准与此类似。若P对每个i标准,则称P标准。P右标准或左标准与此类似(参看[5]、[6])。

Properties of Sample Functions of Denumerable and Nonhomogeneous Markov Processes

In this paper, states of denumerable and nonhomogeneous Markov Processes are divided into stationary and instantaneous, while theorems in pp. 144-160 in[1] are extended to denumerable and nonhomogeneous Markov processes. Moreover, it is shown that states of nonhomogeneous Markov processes in abstract space can be divided in similar manner, and some theorems of sample functions of denumerable and nonhomogeneous Markov processes can be extended to nonhomogeneous Markov processes in abstract space.