The Annals of Probability
- Ann. Probab.
- Volume 20, Number 1 (1992), 1-28.
Necessary and Sufficient Conditions for Sample Continuity of Random Fourier Series and of Harmonic Infinitely Divisible Processes
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.
Ann. Probab., Volume 20, Number 1 (1992), 1-28.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G10: Stationary processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60G17: Sample path properties 42A20: Convergence and absolute convergence of Fourier and trigonometric series 43A50: Convergence of Fourier series and of inverse transforms 42A61: Probabilistic methods
Talagrand, M. Necessary and Sufficient Conditions for Sample Continuity of Random Fourier Series and of Harmonic Infinitely Divisible Processes. Ann. Probab. 20 (1992), no. 1, 1--28. doi:10.1214/aop/1176989916. https://projecteuclid.org/euclid.aop/1176989916