Some Limit Theorems for Functionals of the Brownian Sheet

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.