We study properties of functionals of the Brownian sheet: in particular, we construct square-integrable functionals of $R^d$-valued Brownian sheets, so that $k$-intersection local times on $R^{dk}$ can be obtained as specific examples. Results of central limit theorem type on sums of functionals of Brownian sheets, give us new fields, and we investigate which properties of the Brownian sheet (e.g., Markovianess, renormalizability) these limit fields inherit.
Publié le : 1989-04-14
Classification:
Brownian sheets,
string theory,
square-integrable functionals,
intersection local times,
central limit theorems,
random fields,
60G15,
60G60,
60J55,
60G20
@article{1176991414,
author = {Epstein, Raisa},
title = {Some Limit Theorems for Functionals of the Brownian Sheet},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 538-558},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991414}
}
Epstein, Raisa. Some Limit Theorems for Functionals of the Brownian Sheet. Ann. Probab., Tome 17 (1989) no. 4, pp. 538-558. http://gdmltest.u-ga.fr/item/1176991414/