## The Annals of Probability

### Necessary and Sufficient Conditions for Sample Continuity of Random Fourier Series and of Harmonic Infinitely Divisible Processes

M. Talagrand

#### Abstract

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 information

Source
Ann. Probab., Volume 20, Number 1 (1992), 1-28.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989916

Digital Object Identifier
doi:10.1214/aop/1176989916

Mathematical Reviews number (MathSciNet)
MR1143410

Zentralblatt MATH identifier
0790.60039

JSTOR