On regularization of formal Fourier--Wiener transform of the self-intersection local time of planar Gaussian process

2011/05/19 by Andrey A. Dorogovtsev, Dorogovtsev, Andrey A., Olga L. Izumtseva +2
Mathematics · #60G15 #60H40 #FOS: Mathematics #Probability (math.PR) #advanced mathematical theories #math.PR #msc:60G15 #msc:60H40

paper · pdf · doi:10.48550/arxiv.1105.3892

18 pages

arxiv created 2011/05/19 · openalex publication_date 2011/05/19 · arxiv updated 2011/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fourier-Wiener transform of the formal expression for multiple self-intersection local time is described in terms of the integral, which is divergent on the diagonals. The method of regularization we use in this work related to regularization of functions with non-integrable singularities. The strong local nondeterminism property, which is more restrictive than the property of local nondeterminism introduced by S.Berman is considered. Its geometrical meaning in the construction of the regularization is investigated. As the example the problem of regularization is solved for the compact perturbation of the planar Wiener process.

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