Persistence of Gaussian stationary processes: a spectral perspective

2017/09/01 by Feldheim, Naomi, Feldheim, Ohad, Nitzan, Shahaf · 1 citation
#42A38 #60G10 #60G15 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1709.00204

Abstract

We study the persistence probability of a centered stationary Gaussian process on ℤ or 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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