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The correlated random walk with boundaries: A combinatorial solution

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

W. Böhm
W. Böhm*
Affiliation:
University of Economics, Vienna
*
∗Postal address: Institut fur Statistik, Abteilung fur Mathematische Methoden der Statistik, Augasse 2–6, A 1090 Wien, Austria. Email adress:boehm@isis.wu-wien.ac.at
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Abstract

The transition functions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes.

Keywords

Correlated random walkcombinatorial solutionabsorbing boundaries

MSC classification

Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 470 - 479
Copyright
Copyright © by the Applied Probability Trust 2000 

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