Open Access
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


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.


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Raisa Epstein. "Some Limit Theorems for Functionals of the Brownian Sheet." Ann. Probab. 17 (2) 538 - 558, April, 1989.


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

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

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

Vol.17 • No. 2 • April, 1989
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