Let $\mathbf{X}(t), t \geq 0$, be a vector Gaussian process in $R^m$ whose components are i.i.d. copies of a real Gaussian process $X(t)$ with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity $r$ of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The main tool is the concept of local nondeterminism.
Publié le : 1991-01-14
Classification:
Intersections of sample paths,
local nondeterminism,
local time,
Gaussian processes,
spectral distribution,
60G15,
60G17,
60J55
@article{1176990539,
author = {Berman, Simeon M.},
title = {Self-Intersections and Local Nondeterminism of Gaussian Processes},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 160-191},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990539}
}
Berman, Simeon M. Self-Intersections and Local Nondeterminism of Gaussian Processes. Ann. Probab., Tome 19 (1991) no. 4, pp. 160-191. http://gdmltest.u-ga.fr/item/1176990539/