摘要
Markov链的转移矩阵用条件概率定义。当定义中条件的概率为零时，对条件概率如何补值、以得到一个完整的转移矩阵，同时还要求满足转移矩阵必须满足的非负性、规范性和K-C（kolmogorov-chapman）方程，这就是Markov涟的转移矩阵的补直问题。换句话说，对每个Markov链，是否一定存在完整的转移矩阵？时两参数Markov，例如Poisson单，答案是否定的。对单参数Markov链，本文给出正面的解答。
Transition matrices for a Markov chain are defined withthe aid of conditional probability and must satisfy the conditions (5) (6 ) (7). The conditional probability is undefined,if the probability of the condition is zero. In order toobtain complehensive transition matrices, how do we definetransition probability when conditional probability is undefined.This is the problem replenishing values of transition matricesfor a Markoy chain. In this paper we have solved thisproblem. Let E be a denumerable set, T = { 0, 1, 2, ...} orT = [0. ∞). Let X= {X(t), t∈ E} be a Markov chain with thestate space E. It is proved that P(s, t)= {pif(s, t), i, jE E}.0 ≤s＜t, s, t∈ T, are transition matrices for Markov chain X,where P i j(s, t) is defined by (12), and {u ij(s), i. j∈ E}, s∈ Tsatisfy (8 )(9 )(10), E+(s) and E0(s) are defined by (4).
出处
《益阳师专学报》
1994年第5期1-4,共4页
Journal of Yiyang Teachers College
