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Persistence of Gaussian stationary processes: a spectral perspective
Published 1 Sep 2017 in math.PR and math.FA | (1709.00204v2)
Abstract: We study the persistence probability of a centered stationary Gaussian process on $\mathbb{Z}$ or $\mathbb{R}$, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the behavior of the spectral measure of the process near zero and infinity.
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