If βt is renormalized self-intersection local time for planar Brownian motion, we characterize when $\mathbb{E}e^{\gamma\beta_{1}}$ is finite or infinite in terms of the best constant of a Gagliardo–Nirenberg inequality. We prove large deviation estimates for β1 and −β1. We establish lim sup and lim inf laws of the iterated logarithm for βt as t→∞.
Publié le : 2004-10-14
Classification:
Intersection local time,
Gagliardo–Nirenberg inequality,
law of the iterated logarithm,
critical exponent,
self-intersection local time,
large deviations,
60J55,
60J55,
60F10
@article{1107883352,
author = {Bass, Richard F. and Chen, Xia},
title = {Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 3221-3247},
language = {en},
url = {http://dml.mathdoc.fr/item/1107883352}
}
Bass, Richard F.; Chen, Xia. Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm. Ann. Probab., Tome 32 (2004) no. 1A, pp. 3221-3247. http://gdmltest.u-ga.fr/item/1107883352/