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

Albeverio S, Oliveira MJ, Streit L (2001)
ACTA APPLICANDAE MATHEMATICAE 69(3): 221-241.

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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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Albeverio S, Oliveira MJ, Streit L. Intersection local times of independent Brownian motions as generalized white noise functionals. ACTA APPLICANDAE MATHEMATICAE. 2001;69(3):221-241.
Albeverio, S., Oliveira, M. J., & Streit, L. (2001). Intersection local times of independent Brownian motions as generalized white noise functionals. ACTA APPLICANDAE MATHEMATICAE, 69(3), 221-241. doi:10.1023/A:1014212906782
Albeverio, S., Oliveira, M. J., and Streit, L. (2001). Intersection local times of independent Brownian motions as generalized white noise functionals. ACTA APPLICANDAE MATHEMATICAE 69, 221-241.
Albeverio, S., Oliveira, M.J., & Streit, L., 2001. Intersection local times of independent Brownian motions as generalized white noise functionals. ACTA APPLICANDAE MATHEMATICAE, 69(3), p 221-241.
S. Albeverio, M.J. Oliveira, and L. Streit, “Intersection local times of independent Brownian motions as generalized white noise functionals”, ACTA APPLICANDAE MATHEMATICAE, vol. 69, 2001, pp. 221-241.
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).
Albeverio, Sergio, Oliveira, MJ, and Streit, Ludwig. “Intersection local times of independent Brownian motions as generalized white noise functionals”. ACTA APPLICANDAE MATHEMATICAE 69.3 (2001): 221-241.
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