The Annals of Probability

The Integral of the Absolute Value of the Pinned Wiener Process-- Calculation of Its Probability Density by Numerical Integration

S. O. Rice

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Abstract

L. A. Shepp [1] has studied the distribution of the integral of the absolute value of the pinned Wiener process, and has expressed the moment generating function in terms of a Laplace transform. Here we apply Shepp's results to obtain an integral for the density of the distribution. This integral is then evaluated by numerical integration along a path in the complex plane.

Article information

Source
Ann. Probab., Volume 10, Number 1 (1982), 240-243.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993927

Digital Object Identifier
doi:10.1214/aop/1176993927

Mathematical Reviews number (MathSciNet)
MR637390

Zentralblatt MATH identifier
0479.60080

JSTOR
links.jstor.org

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 65D30: Numerical integration 60J65: Brownian motion [See also 58J65] 65E05: Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see also 30C30}

Keywords
Pinned Wiener process probability density of an integral numerical integration in the complex plane

Citation

Rice, S. O. The Integral of the Absolute Value of the Pinned Wiener Process-- Calculation of Its Probability Density by Numerical Integration. Ann. Probab. 10 (1982), no. 1, 240--243. doi:10.1214/aop/1176993927. https://projecteuclid.org/euclid.aop/1176993927


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