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Some exact distributions of a last one-sided exit time in the simple random walk

Published online by Cambridge University Press:  14 July 2016

Chern-Ching Chao  and
John Slivka
Chern-Ching Chao
Affiliation:
State University of New York at Buffalo
John Slivka*
Affiliation:
State University of New York at Buffalo
*
∗∗Postal address: Department of Mathematics, State University College, 1300 Elmwood Avenue, Buffalo, NY 14222, USA.
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Abstract

For each positive integer n, let Sn be the nth partial sum of a sequence of i.i.d. random variables which assume the values +1 and −1 with respective probabilities p and 1 – p, having mean μ= 2p − 1. The exact distribution of the random variable , where sup Ø= 0, is given for the case that λ > 0 and μ+ λ= k/(k + 2) for any non-negative integer k. Tables to the 99.99 percentile of some of these distributions, as well as a limiting distribution, are given for the special case of a symmetric simple random walk (p = 1/2).

Keywords

STRONG LAW OF LARGE NUMBERSSUMS OF I.I.D. BERNOULLI VARIABLESLINEAR BOUNDARY CROSSINGSLAST DEVIATION
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 332 - 340
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

∗

Present address: Department of Statistics, University of Kentucky, Lexington, KY 40506, USA.

This investigation was partially supported by a Research Development Fund Award from the State University of New York Research Foundation.

References

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