Geodesic
On self-intersection local times for generalized Brownian bridges and the distance between step functions
Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 1-13

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In the paper $k$-multiple self-intersection local time for planar Gaussian integrators generated by linear operator with nontrivial kernel is studied. In this case additional singularities arise in its formal Fourier-Wiener transform. In case $k=2$ the set of singularities is the finite number of points. In case $k>2$ it contains intervals and hyperplanes. In the first and the second cases using two different approaches related on structure of set of singularities we show that "new" singularities do not imply on the convergence of integral corresponding to the formal Fourier-Wiener transform and regularization consist of compensation of impact of diagonals as for the Wiener process.
Keywords: Gaussian integrators, white noise, self-intersection local time
Mots-clés : Fourier-Wiener transform. 
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     title = {On self-intersection local times for generalized {Brownian} bridges and the distance between step functions},
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A. A. Dorogovtsev; O. L. Izyumtseva. On self-intersection local times for generalized Brownian bridges and the distance between step functions. Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a0/