On large increments of infinite series of Ornstein-Uhlenbeck processes (Q1909961)

Let \(G(t)\) be a stationary Gaussian process with mean 0, nondecreasing function \(\sigma^2 (s) = E(G(s + t) - G(t))^2\), covariance \(EG(s) G(0) \to 0\) as \(s \to \infty\) and finite integral \(\int^\infty_1 \sigma (\exp \{- x^2\}) dx\). Strong limit results for large increments of \(G(t)\), analogous to that concerning moduli of continuity, established by \textit{E. Csáki}, \textit{M. Csörgö}, the author and \textit{P. Révész} [Stochastic Processes Appl. 39, No. 1, 25-44 (1991; Zbl 0745.60036)], are obtained. Next they are applied to the process \(\sum^\infty_{k = 1} X_k (t)\), where \((X_k (t))\) is a sequence of independent Ornstein-Uhlenbeck processes.