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

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.