Intersection local times of independent Brownian motions as generalized white noise functionals

Albeverio, Sergio; Oliveira, Maria João; Streit, Ludwig

http://hdl.handle.net/10400.2/1670

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Authors

Albeverio, Sergio

Oliveira, Maria João

Streit, Ludwig

Abstract(s)

A "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their Lp-properties are discussed. An important tool for deriving the chaos expansion is a computation of the "S-transform" of the corresponding regularized intersection local times and a control about their singular limit.

Description

The original publication is available at http://www.springerlink.com/content/14jtbl19nh37ggtx/fulltext.pdf

Keywords

Intersection local times Brownian motion Chaos expansion White noise functionals Polymers Quantum fields Donsker's δ-function Hida distributions

URI

http://hdl.handle.net/10400.2/1670

Citation

Albeverio, Serigio; Oliveira, Maria João; Streit, Ludwing - Intersection local times of independent Brownian motions as generalized white noise functionals. "Acta Applicandae Mathematicae" [Em linha]. ISSN 0167-8019 (Print) 1572-9036 (Online). Vol. 69, nº 3 (2001), p. 221-241