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Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

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Abstract

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R d 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 L p-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.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, D 53115, Bonn, Germany

    Sergio Albeverio

  2. Ruhr-Universität Bochum, Germany

    Sergio Albeverio

  3. BiBoS, Universität Bielefeld, D 33501, Bielefeld, Germany

    Sergio Albeverio, Maria João Oliveira & Ludwig Streit

  4. SFB 256 and SFB 237, Germany

    Sergio Albeverio

  5. CERFIM (, Locarno

    Sergio Albeverio

  6. USI (, Mendrisio

    Sergio Albeverio

  7. Grupo de Física Matemática, Univ. Aberta, Av. Prof. Gama Pinto, 2, P 1649-003, Lisbon, Portugal

    Maria João Oliveira

  8. CCM, Universidade da Madeira, P 9000, Funchal, Portugal

    Ludwig Streit

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  1. Sergio Albeverio
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  2. Maria João Oliveira
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  3. Ludwig Streit
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Albeverio, S., Oliveira, M.J. & Streit, L. Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae 69, 221–241 (2001). https://doi.org/10.1023/A:1014212906782

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