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Continuity Properties of Some Gaussian Processes

Continuity Properties of Some Gaussian Processes,10.1214/aoms/1177692721,The Annals of Mathematical Statistics,Christopher Preston

Continuity Properties of Some Gaussian Processes   (Citations: 18)
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Let $(S, d)$ be a compact metric space; let $(\Omega, \mathscr{F}, P)$ be a probability space, and for each $t \in S$ let $X_t: \Omega \rightarrow \mathbb{R}$ be a random variable, with $E(X_t) = 0$ and such that $\{X_t\}_{t\in S}$ forms a Gaussian process. In this paper we find sufficient conditions for the Gaussian process $\{X_t\}_{t\in S}$ to admit a separable and measurable model whose sample functions are continuous with probability one. The conditions involve the covariance, $E(X_s, X_t)$, of the process and also the $\varepsilon$-entropy of $S$.
Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 285-292, 1972
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