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

Johnson, B. McK.; Killeen, T.

Ann. Probab., Tome 11 (1983) no. 4, p. 807-808 / Harvested from Project Euclid

Résumé

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.

Publié le : 1983-08-14
Classification: Brownian bridge, $L_1$ norm, 60G15, 60E05

@article{1176993528,
     author = {Johnson, B. McK. and Killeen, T.},
     title = {An Explicit Formula for the C.D.F. of the $L\_1$ Norm of the Brownian Bridge},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 807-808},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993528}
}

Johnson, B. McK.; Killeen, T. An Explicit Formula for the C.D.F. of the $L_1$ Norm of the Brownian Bridge. Ann. Probab., Tome 11 (1983) no. 4, pp.  807-808. http://gdmltest.u-ga.fr/item/1176993528/