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This article is cited in 2 scientific papers (total in 2 papers)
On regularization of the formal Fourier–Wiener transform of the self-intersection local time of a planar Gaussian process
A. A. Dorogovtsev, O. L. Izyumtseva Institute of Mathematics of the Ukrainian Academy of Sciences, Kiev, Ukraine
Abstract:
The Fourier–Wiener transform of the formal expression for a multiple self-intersection local time is described in terms of an integral, which is divergent on the diagonals. The method of regularization we used in this work is related to the regularization of functions with nonintegrable 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 an example, the problem of regularization is solved for a compact perturbation of the planar Wiener process.
Keywords:
Multiple self-intersection local time, Fourier–Wiener transform, local nondeterminism.
Citation:
A. A. Dorogovtsev, O. L. Izyumtseva, “On regularization of the formal Fourier–Wiener transform of the self-intersection local time of a planar Gaussian process”, Theory Stoch. Process., 17(33):1 (2011), 28–38
Linking options:
https://www.mathnet.ru/eng/thsp38 https://www.mathnet.ru/eng/thsp/v17/i1/p28
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Abstract page: | 167 | Full-text PDF : | 45 | References: | 29 |
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