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.
Publié le : 1982-02-14
Classification:
Pinned Wiener process,
probability density of an integral,
numerical integration in the complex plane,
60H05,
65D30,
60J65,
65E05
@article{1176993927,
author = {Rice, S. O.},
title = {The Integral of the Absolute Value of the Pinned Wiener Process-- Calculation of Its Probability Density by Numerical Integration},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 240-243},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993927}
}
Rice, S. O. The Integral of the Absolute Value of the Pinned Wiener Process-- Calculation of Its Probability Density by Numerical Integration. Ann. Probab., Tome 10 (1982) no. 4, pp. 240-243. http://gdmltest.u-ga.fr/item/1176993927/