Some fluctuation results are proved for the volume of the Wiener sausage associated with a $d$-dimensional Brownian motion and a compact set of positive capacity. In high dimensions, the limiting distribution is normal, whereas, if $d = 2$, it is that of a renormalized local time of self-intersections of planar Brownian motion. For $d = 2$ or 3, these limit theorems are closely linked with the renormalization results for self-intersections of Brownian paths.
Publié le : 1988-07-14
Classification:
Brownian motion,
Wiener sausage,
fluctuation results,
intersection local time,
renormalization,
60J65,
60F05,
60G17
@article{1176991673,
author = {Gall, Jean-Francois Le},
title = {Fluctuation Results for the Wiener Sausage},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 991-1018},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991673}
}
Gall, Jean-Francois Le. Fluctuation Results for the Wiener Sausage. Ann. Probab., Tome 16 (1988) no. 4, pp. 991-1018. http://gdmltest.u-ga.fr/item/1176991673/