The Annals of Probability

An Explicit Formula for the C.D.F. of the $L_1$ Norm of the Brownian Bridge

B. McK. Johnson and T. Killeen

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Abstract

Let $X(t), 0 \leq t \leq 1$, be the Brownian bridge and $L = \int^1_0 |X(t)| dt$. Using results of Shepp [5] and Rice [4], an explicit formula for $P(L \leq \ell)$ is obtained.

Article information

Source
Ann. Probab., Volume 11, Number 3 (1983), 807-808.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993528

Digital Object Identifier
doi:10.1214/aop/1176993528

Mathematical Reviews number (MathSciNet)
MR704570

Zentralblatt MATH identifier
0516.60044

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60E05: Distributions: general theory

Keywords
Brownian bridge $L_1$ norm

Citation

Johnson, B. McK.; Killeen, T. An Explicit Formula for the C.D.F. of the $L_1$ Norm of the Brownian Bridge. Ann. Probab. 11 (1983), no. 3, 807--808. doi:10.1214/aop/1176993528. https://projecteuclid.org/euclid.aop/1176993528


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