The Annals of Applied Probability

On the Distribution of the Integral of the Absolute Value of the Brownian Motion

Lajos Takacs

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Abstract

Kac has considered the integral of the absolute value of a Brownian motion process and determined the Laplace-Stieltjes transform of the distribution function of this integral. In this paper explicit expressions are given for the distribution and the moments of this integral.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 1 (1993), 186-197.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005514

Digital Object Identifier
doi:10.1214/aoap/1177005514

Mathematical Reviews number (MathSciNet)
MR1202522

Zentralblatt MATH identifier
0776.60051

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes

Keywords
Brownian motion integral of the absolute value of the process distribution moments

Citation

Takacs, Lajos. On the Distribution of the Integral of the Absolute Value of the Brownian Motion. Ann. Appl. Probab. 3 (1993), no. 1, 186--197. doi:10.1214/aoap/1177005514. https://projecteuclid.org/euclid.aoap/1177005514


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