no. 2
Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions
Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 117-141.

Soit {X(t),t∈[0,1] n } un processus gaussien séparable et stochastiquement continu, satisfaisant à la condition E[X(t+h)-X(t)] 2 =σ 2 (|h|). On obtient une condition suffisante de continuité presque sûre de X(t), mise en termes de ré-arrangement monotone de σ. On fait l’application de ce résultat aux séries des fonctions aléatoires, en particulier, aux séries aléatoires de Fourier.

Let {X(t),t∈[0,1] n } be a stochastically continuous, separable, Gaussian process with E[X(t+h)-X(t)] 2 =σ 2 (|h|). A sufficient condition, in terms of the monotone rearrangement of σ, is obtained for X(t) to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.

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     author = {Jain, Naresh C. and Marcus, Michael B.},
     title = {Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions},
     journal = {Annales de l'Institut Fourier},
     pages = {117--141},
     publisher = {Institut Fourier},
     address = {Grenoble},
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     year = {1974},
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Jain, Naresh C.; Marcus, Michael B. Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 117-141. doi : 10.5802/aif.508. https://aif.centre-mersenne.org/articles/10.5802/aif.508/

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