零常返Markov链的首回速度

The First Returning Speed of Null Recurrent Markov Chains

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.