Displaying similar documents to “A post-predictive view of gaussian processes”

Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions

Naresh C. Jain, Michael B. Marcus (1974)

Annales de l'institut Fourier

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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.