We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.
Publié le : 1977-02-14
Classification:
Brownian motion,
Brownian meander,
Brownian bridge,
Brownian excursion,
distribution of supremum,
weak convergence,
60J65,
60B10
@article{1176995895,
author = {Durrett, Richard T. and Iglehart, Donald L. and Miller, Douglas R.},
title = {Weak Convergence to Brownian Meander and Brownian Excursion},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 117-129},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995895}
}
Durrett, Richard T.; Iglehart, Donald L.; Miller, Douglas R. Weak Convergence to Brownian Meander and Brownian Excursion. Ann. Probab., Tome 5 (1977) no. 6, pp. 117-129. http://gdmltest.u-ga.fr/item/1176995895/