Open Access
Translator Disclaimer
April, 1989 Some Limit Theorems for Functionals of the Brownian Sheet
Raisa Epstein
Ann. Probab. 17(2): 538-558 (April, 1989). DOI: 10.1214/aop/1176991414

Abstract

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.

Citation

Download Citation

Raisa Epstein. "Some Limit Theorems for Functionals of the Brownian Sheet." Ann. Probab. 17 (2) 538 - 558, April, 1989. https://doi.org/10.1214/aop/1176991414

Information

Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0711.60046
MathSciNet: MR985377
Digital Object Identifier: 10.1214/aop/1176991414

Subjects:
Primary: 60G15
Secondary: 60G20 , 60G60 , 60J55

Keywords: Brownian sheets , central limit theorems , intersection local times , Random fields , square-integrable functionals , string theory

Rights: Copyright © 1989 Institute of Mathematical Statistics

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.17 • No. 2 • April, 1989
Back to Top