Stationary Gaussian processes with a finite correlation function

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Abstract

If the correlation function vanishes outside the segment [-R, R], then an upper estimate (uniform with respect to all such processes) is possible for the probability of the fact that on an other segment [-r, r] the process remains between - ε and ε. Such an estimate is obtained, decreasing for ε → 0 as exp(-f(r/Rln2+ ∞) and, moreover, r/R may be either 0 or +∞. The proof is based on an estimate of the form ∥ PmQn ∥ ≥ cmn ∥ Pm∥{dot operator} ∥ Qn ∥ for norms of polynomials on a circle in the complex plane.

Original languageEnglish
Pages (from-to)597-603
Number of pages7
JournalJournal of Mathematical Sciences
Volume68
Issue number4
DOIs
StatePublished - Feb 1994

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