摘要
对零常返Markov链的首回速度进行了讨论.首先用n步转移概率{pxx(n)}刻画了Ex[w(τx)]有限的条件,这里τx是状态x的首回时,w是一个正函数.其次研究了与电网紧密联系的可逆Markov链,用一些有效电导给出点Ex[w,(τx)]有限的等价条件,并给出一些比较法则.
This paper is devoted to discuss the first returning speed of the null recurrent Markov chains. Firstly, the author characterizes the finiteness of Ex [w(Tx)] by means of the n-step transition probabilities {p(n)xx}, where Tx is the first returning time to x and w is a positive function, and studies the reversible Markov chains which relate to electric networks. An equivalent condition for the finiteness of Ex [w(Tx)] is obtained by means of some effective conductances. Also some monotonicity laws are given.
出处
《数学年刊(A辑)》
CSCD
北大核心
2006年第6期761-770,共10页
Chinese Annals of Mathematics
关键词
MARKOV链
零常返
首回时
电网
Markov chain, Null recurrent, First returning time, Electric network