Let $b^F(t)$; $t \in [0,1]$ be an $F$-Brownian bridge process. We study the asymptotic behaviour of non-linear functionals of regularizations by convolution of this process and apply these results to the estimation of the variance of a non-homogeneous diffusion and to the convergence of the number of crossings of a level by the regularized process to a modification of the local time of the Brownian bridge as the regularization parameter goes to 0.
Publié le : 2001-03-05
Classification:
Non-homogeneous difusion,
Brownian bridge,
Non-linear functionals,
Regularization by convolution,
Crossings,
Local time,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00319148,
author = {Berzin-Joseph, Corinne and Le\'on, Jos\'e R. and Ortega, Joaqu\'\i n},
title = {Non-linear functionals of the Brownian bridge and some applications},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00319148}
}
Berzin-Joseph, Corinne; León, José R.; Ortega, Joaquín. Non-linear functionals of the Brownian bridge and some applications. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00319148/