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 Electronic Communications in Probability > Vol. 6 (2001) > Paper 7 open journal systems 


Pitman's 2M-X Theorem for Skip-Free Random Walks with Markovian Increments

B. M. Hambly, University of Oxford
James B. Martin, Cambridge University
Neil O'Connell, BRIMS, HP Labs


Abstract
Let $(xi_k, kge 0)$ 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 $M_n=max_{0le kle n}X_k$. We prove that the process $2M-X$ has the same law as that of $X$ conditioned to stay non-negative.


Full text: PDF

Pages: 73-77

Published on: August 21, 2001
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Electronic Communications in Probability. ISSN: 1083-589X