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Another visit to two halflines

Published online by Cambridge University Press:  01 July 2016

G. Hooghiemstra
G. Hooghiemstra*
Affiliation:
Delft University of Technology
*
∗Postal address: Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands.
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Abstract

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We shall use three basic properties of Brownian motion to derive in an elegant and non-computational way the probability that standard Brownian motion, starting from 0, will ever cross the halflines t → αt + β or t → γt + δ where γ, δ < 0 < α, β.

Keywords

BOUNDARY CROSSINGBROWNIAN MOTIONKOLMOGOROV–SMIRNOV STATISTICS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 935 - 937
Copyright
Copyright © Applied Probability Trust 1989 

References

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Durbin, J. (1973) Distribution Theory for Test Based on the Sample Distribution Function. SIAM, Philadelphia.Google Scholar
Hooghiemstra, G. (1987) On functionals of the adjusted range process. J. Appl. Prob. 24, 252–257.Google Scholar