Random sequences with normal covariances

Jiří Michálek

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Let ${X (t), t \in [0, 1]^{n}}$ 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.