The Annals of Applied Probability

On a generalization of the arc-sine law

Lajos Takács

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This paper deals with the distribution function of the sojourn time of Brownian motion with drift. By some recent results of J. Akahori and A. Dassios this distribution function can be expressed in the form of a double integral. In this paper it is shown that the distribution function of the sojourn time can be expressed simply as a single integral. The result obtained is a generalization of the arc-sine law of Paul Lévy.

Article information

Ann. Appl. Probab. Volume 6, Number 3 (1996), 1035-1040.

First available: 18 October 2002

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Zentralblatt MATH identifier

Primary: 60J15 60J55: Local time and additive functionals 60J65: Brownian motion [See also 58J65]

Random walk Brownian motion sojourn time distribution function


Takács, Lajos. On a generalization of the arc-sine law. The Annals of Applied Probability 6 (1996), no. 3, 1035--1040. doi:10.1214/aoap/1034968240.

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