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A Note on Absorption Probabilities for a Random Walk Between a Reflecting and an Absorbing Barrier

Published online by Cambridge University Press:  14 July 2016

J.C. Hardin  and
A.L. Sweet
J.C. Hardin
Affiliation:
Purdue University
A.L. Sweet
Affiliation:
Purdue University
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Extract

Generating functions for the absorption probabilities for a random walk on the integers {0,1, …, b}, where 0 is an absorbing barrier and b a semi-reflecting barrier have been obtained by Weesakul [1] and Neuts [2]. However, determination of explicit expressions for the absorption probabilities from the generating functions is generally quite difficult. In this note, two cases where this is possible are presented.

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 224 - 226
Copyright
Copyright © Applied Probability Trust 

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References

[1] Weesakul, B. (1961) The random walk between a reflecting and an absorbing barrier Ann. Math. Statist. 32, 765–769.CrossRefGoogle Scholar
[2] Neuts, M. F. (1963) Absorption probabilities for a random walk between a reflecting and an absorbing barrier. Bull. Soc. Math. Belg. 15, 253–258.Google Scholar