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A reconciliation of two different expressions for the first-passage density of brownian motion to a curved boundary

Published online by Cambridge University Press:  14 July 2016

J. Durbin
J. Durbin*
Affiliation:
London School of Economics and Political Science
*
∗Postal address: Department of Statistical and Mathematical Sciences, London School of Economics and Political Science, Houghton St., London WC2A 2AE.
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Abstract

An expression for the first-passage density of Brownian motion to a curved boundary due to Daniels and Lerche is shown to give the same result as a different form due to the author. The equivalence is extended to continuous Gaussian Markov processes.

Keywords

METHOD OF IMAGESCONTINUOUS GAUSSIAN PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 829 - 832
Copyright
Copyright © Applied Probability Trust 1988 

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References

Daniels, H. E. (1969) The minimum of a stationary Markov process superimposed on a U-shaped trend. J. Appl. Prob. 6, 399–408.Google Scholar
Daniels, H. E. (1982) Sequential tests constructed from images. Ann. Statist. 10, 394–400.Google Scholar
Doob, J. L. (1949) Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statist. 20, 393–403.Google Scholar
Durbin, J. (1985) The first passage density of a continuous Gaussian process to a general boundary. J. Appl. Prob. 22, 99–122.CrossRefGoogle Scholar
Lerche, R. (1986) Boundary Crossing of Brownian Motion. Lecture Notes in Statistics 40. Springer-Verlag, Heidelberg.Google Scholar
Mehr, C. B. and Mcfadden, J. A. (1965) Certain properties of Gaussian processes and their first-passage times. J. R. Statist. Soc. B 27, 505–522.Google Scholar