文章基本信息

标题：Pitman's $2M-X$ Theorem for Skip-Free Random Walks with Markovian Increments
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作者：Hambly, B. M. ; Martin, James B. ; O'Connell, Neil 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2001
卷号：6
页码：73-77
DOI：10.1214/ECP.v6-1036
出版社：Electronic Communications in Probability
摘要：Let $(\xi_k, k\ge 0)$ be a Markov chain on ${-1,+1}$ with $\xi_0=1$ and transition probabilities $P(\xi_{k+1}=1| \xi_k=1)=a>b=P(\xi_{k+1}=-1| \xi_k=-1)$. Set $X_0=0$, $X_n=\xi_1+\cdots +\xi_n$ and $M_n=\max_{0\le k\le n}X_k$. We prove that the process $2M-X$ has the same law as that of $X$ conditioned to stay non-negative.
关键词：Pitman's representation, three-dimensional Bessel process,telegrapher's equation, queue, Burke's theorem, quasireversibility.;60J10, 60J27, 60J45, 60K25