Displaying similar documents to “Continuous factorizations of covariance operators and 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.

Abel means of operator-valued processes

G. Blower (1995)

Studia Mathematica

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Let ( X j ) be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of X n . . . X 2 X 1 to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.