IX: 14, 318-335, LNM 465 (1975)
FERNIQUE, Xavier
Des résultats nouveaux sur les processus gaussiens (Gaussian processes)
Given a centered Gaussian process indexed by an arbitrary set~$T$, a major problem has been to find conditions implying that the sample functions are a.s. bounded, or a.s. continuous in the natural metric associated with the covariance. Here new necessary conditions for boundedness are given, which turn out to be sufficient in the case of stationary processes on $R^n$. The conditions given here involve the existence of a majorizing measure, an idea which became crucial in the theory
Comment: For a systematic account of the theory around the time this paper was written, see Fernique's lectures in École d'Été de Saint-Four~IV, LNM 480, 1974. For the definitive solution, see chapter 11 of Ledoux-Talagrand Probability in Banach spaces, Springer 1991
Keywords: Gaussian processes, Sample path regularity
Nature: Original
Retrieve article from Numdam

---