Some limit theorems for functionals of the Brownian sheet. (English) Zbl 0711.60046

Epstein, Raisa

Ann. Probab. 17, No. 2, 538-558 (1989).

This paper is concerned with the construction of square-integrable functionals of Brownian sheets, to establish limit theorems for sums of these functionals, and to investigate the “local times” and “intersection local times” of several sheets.
This theory is formally analogous to the theory for Brownian motion, but requires new definitions, new concepts, and new techniques. The paper is motivated by physics, specifically interacting random surfaces, falling within the rubic “gauge theory”.

Reviewer: P.Protter

MSC:

60G60	Random fields
60G15	Gaussian processes
60J55	Local time and additive functionals
60G20	Generalized stochastic processes

Keywords:

Brownian sheets; local times; intersection local times; interacting random surfaces; gauge theory