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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 processes

Nature: Original

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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 processes

Nature: Original

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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

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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 eigenvalues

Nature: Original

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 processes

Nature: Original

Retrieve article from Numdam

VIII: 12, 155-171, LNM 381 (1974)

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 processes

Nature: Original

Retrieve article from Numdam

IX: 14, 318-335, LNM 465 (1975)

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 $

Comment: For a systematic account of the theory around the time this paper was written, see Fernique's lectures in

Keywords: Gaussian processes, Sample path regularity

Nature: Original

Retrieve article from Numdam

XLIV: 19, 409-428, LNM 2046 (2012)

Large deviations for Gaussian stationary processes and semi-classical analysis (Limit theorems, theory of processes)

Keywords: Large deviations, Gaussian processes, Toeplitz matrices, Distribution of eigenvalues

Nature: Original