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A boundary-crossing result for Brownian motion

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Thomas H. Scheike
Thomas H. Scheike*
Affiliation:
University of Copenhagen
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Abstract

In this paper we obtain a new crossing result for Brownian motion. The boundary studied is a piecewise linear function consisting of two lines. The expression obtained for the boundary crossing probability is of a simple directly computable form.

Keywords

BOUNDARY-CROSSING PROBABILITYPIECEWISE LINEAR BOUNDARY

MSC classification

Primary: 60J75: Jump processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 448 - 453
Copyright
Copyright © Applied Probability Trust 1992 

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References

Daniels, H. E. (1982) Sequential tests constructed from images. Ann. Statist. 10, 394–400.Google Scholar
Durbin, J. (1985) The first passage density of a continuous Gaussian process to a general boundary. J. Appl. Prob. 22, 99–122.Google Scholar
Lerche, H. R. (1986) Boundary Crossing of Brownian Motion. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Robbins, H. and Siegmund, D. (1970) Boundary crossing probabilities for the Wiener process and partial sums. Ann. Math. Statist. 41, 1410–1429.CrossRefGoogle Scholar