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Another visit to two halflines

Published online by Cambridge University Press:  01 July 2016

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 tαt + β or tγt + δ where γ, δ < 0 < α, β.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1989 

References

Doob, J. L. (1949) Heuristic approach to the Kolmogorov–Smirnov theorems. Ann. Math. Statist. 20, 393403.CrossRefGoogle Scholar
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, 252257.Google Scholar