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A boundary-crossing result for Brownian motion

  • Thomas H. Scheike (a1)

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.

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References

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Daniels, H. E. (1982) Sequential tests constructed from images. Ann. Statist. 10, 394400.
Durbin, J. (1985) The first passage density of a continuous Gaussian process to a general boundary. J. Appl. Prob. 22, 99122.
Lerche, H. R. (1986) Boundary Crossing of Brownian Motion. Springer-Verlag, Berlin.
Robbins, H. and Siegmund, D. (1970) Boundary crossing probabilities for the Wiener process and partial sums. Ann. Math. Statist. 41, 14101429.

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A boundary-crossing result for Brownian motion

  • Thomas H. Scheike (a1)

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