VII: 10, 77-94, LNM 321 (1973)
HEINKEL, Bernard
Une condition suffisante pour la continuité presque sûre des trajectoires de certains processus gaussiens (
Gaussian processes)
It is shown that a continuity criterion due to Preston (1972) can be deduced from a theorem of Dudley (1967)
Comment: To be completed
Keywords: Continuity of paths of Gaussian processesNature: Original
Retrieve article from Numdam
VIII: 12, 155-171, LNM 381 (1974)
HEINKEL, Bernard
Théorèmes de dérivation du type de Lebesgue et continuité presque sûre de certains processus gaussiens (
Gaussian processes)
To be completed
Comment: To be completed
Keywords: Continuity of paths of Gaussian processesNature: Original Retrieve article from Numdam
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 regularityNature: Original Retrieve article from Numdam
XLIV: 19, 409-428, LNM 2046 (2012)
BERCU, Bernard;
BONY, Jean-François;
BRUNEAU, Vincent
Large deviations for Gaussian stationary processes and semi-classical analysis (
Limit theorems,
theory of processes)
Keywords: Large deviations,
Gaussian processes,
Toeplitz matrices,
Distribution of eigenvaluesNature: Original
