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August 1996 On a generalization of the arc-sine law
Lajos Takács
Ann. Appl. Probab. 6(3): 1035-1040 (August 1996). DOI: 10.1214/aoap/1034968240

Abstract

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.

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Lajos Takács. "On a generalization of the arc-sine law." Ann. Appl. Probab. 6 (3) 1035 - 1040, August 1996. https://doi.org/10.1214/aoap/1034968240

Information

Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0860.60051
MathSciNet: MR1410128
Digital Object Identifier: 10.1214/aoap/1034968240

Subjects:
Primary: 60J15 , 60J55 , 60J65

Keywords: Brownian motion , distribution function , Random walk , sojourn time

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 3 • August 1996
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