## The Annals of Probability

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

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

#### 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