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This paper is concerned with the probability, PT, r(τ), that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P are given, along with some comparison theorems that relate P's for different covariance functions. Similar results are given for FT, r(τ), the probability distribution for the interval between two successive zeros of the process.
D. Slepian (Thu,) studied this question.
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