For very general random Fourier series and infinitely divisible processes on a locally compact Abelian group $G$, a necessary and sufficient condition for sample continuity is given in terms of the convergence of a certain series. This series expresses a control on the covering numbers of a compact neighborhood of $G$ by certain nonrandom sets naturally associated with the Fourier series (resp. the process). In the nonstationary case, we give a necessary Sudakov-type condition for a probability measure in a Banach space to be a Levy measure.
@article{1176989916,
author = {Talagrand, M.},
title = {Necessary and Sufficient Conditions for Sample Continuity of Random Fourier Series and of Harmonic Infinitely Divisible Processes},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1-28},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989916}
}
Talagrand, M. Necessary and Sufficient Conditions for Sample Continuity of Random Fourier Series and of Harmonic Infinitely Divisible Processes. Ann. Probab., Tome 20 (1992) no. 4, pp. 1-28. http://gdmltest.u-ga.fr/item/1176989916/