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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

Darling, D. A. (1960) On the theorems of Kolmogorov-Smirnov. Theory Prob. Appl. 5, 356–361.CrossRefGoogle Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Miller, L. (1956) Percentage points of Kolmogorov statistics. J. Amer. Statist. Assoc. 51, 111–121.Google Scholar
Petrov, V. V. (1972) Sum of Independent Random Variables. Springer-Verlag, Berlin.Google Scholar
Siegmund, D. (1979) Corrected diffusion approximations in certain random walk problems. Adv. Appl. Prob. 11, 701–719.Google Scholar
Smirnov, N. V. (1944) An approximation to the distribution laws of random quantities determined by empirical data. Uspehi Mat. Nauk. 10, 179–206.Google Scholar