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Generating functions for a class of one-dimensional random walks

Published online by Cambridge University Press:  14 July 2016

Ora Engelberg Percus  and
Jerome K. Percus
Ora Engelberg Percus
Affiliation:
City College, City University of New York
Jerome K. Percus
Affiliation:
Courant Institute of Mathematical Sciences, New York University
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Abstract

A weighted Markov chain technique is used to find the generating functions for several restricted one-dimensional random walks. Examples with simple restrictions concern the number of penetrations of a penetrable barrier. Examples with compound restrictions include the number of full crossings of the origin. A typical asymptotic evaluation is carried out.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 110 - 117
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Percus, O. E. and Percus, J. K. (1969) On the distribution of the number of zero partial sums. J. Appl. Prob. 6, 162–176.Google Scholar
[2] Percus, O. E. and Percus, J. K. (1970) Extended criterion for comparison of empirical distributions. J. Appl. Prob. 7, 1–20.CrossRefGoogle Scholar
[3] Engelberg, O. (1965) Generalizations of the ballot problem. Z. Wahrscheinlichkeitsth. 3, 271–275.Google Scholar
[4] Riordan, J. (1964) The enumeration of election returns by number of lead positions Ann. Math. Statist. 35, 369–379.Google Scholar
[5] Engelberg, O. (1965) On some problems concerning a restricted random walk. J. Appl. Prob. 2, 396–404.Google Scholar