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Second-order corrections for Brownian motion approximations to first-passage probabilities

Published online by Cambridge University Press:  01 July 2016

Yih-Shyh Yuh
Yih-Shyh Yuh*
Affiliation:
University of California, San Diego
*
∗Dr Yuh died on 5 June 1981, before she could revise this paper. The revision was prepared by Dr James Koziol, Biostatistics, M-022A, University of California, San Diego, La Jolla, CA 92093, U.S.A., to whom reprint requests should be sent.
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Abstract

Correction terms are obtained for the Brownian motion approximation to one- and two-barrier first-passage probabilities. These approximations are given in terms of their Laplace transforms, which are formally (and non-rigorously) inverted. Applications to the one-sample Kolmogorov-Smirnov statistic are discussed.

Keywords

BROWNIAN MOTION APPROXIMATIONRANDOM WALKLAPLACE TRANSFORMFIRST-PASSAGE PROBABILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 566 - 581
Copyright
Copyright © Applied Probability Trust 1982 

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References

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