A class of random fields associated with multiple points of a random walk in the plane is studied. It is proved that these fields converge in distribution to analogous fields measuring self-intersections of the planar Brownian motion. The concluding section contains a survey of literature on intersection local times and their renormalizations. A brief look through the first pages of this section could provide the reader with additional motivation for the present work.
Publié le : 1988-01-14
Classification:
Self-intersection local times,
self-intersection gauges,
the invariance principle,
multiple points of random walks and of the Brownian motion,
60G60,
60J55,
60J65
@article{1176991884,
author = {Dynkin, E. B.},
title = {Self-Intersection Gauge for Random Walks and for Brownian Motion},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1-57},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991884}
}
Dynkin, E. B. Self-Intersection Gauge for Random Walks and for Brownian Motion. Ann. Probab., Tome 16 (1988) no. 4, pp. 1-57. http://gdmltest.u-ga.fr/item/1176991884/