The distribution of the integral of the absolute value of the
Brownian bridge was expressed by Cifarelli and independently by Johnson and
Killeen in the form of a series. Rice obtained the corresponding probability
density by numerical integration. Here we determine the exact tail asymptotics
of this distribution, as well as the exact asymptotics of its density function
for the large values of the argument.
@article{1019160114,
author = {Tolmatz, Leonid},
title = {Asymptotics of the distribution of the integral of the absolute
value of the Brownian bridge for large arguments},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 132-139},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160114}
}
Tolmatz, Leonid. Asymptotics of the distribution of the integral of the absolute
value of the Brownian bridge for large arguments. Ann. Probab., Tome 28 (2000) no. 1, pp. 132-139. http://gdmltest.u-ga.fr/item/1019160114/