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May 2021 Persistence of Gaussian stationary processes: A spectral perspective
Naomi Feldheim, Ohad Feldheim, Shahaf Nitzan
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Ann. Probab. 49(3): 1067-1096 (May 2021). DOI: 10.1214/20-AOP1470

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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Naomi Feldheim. Ohad Feldheim. Shahaf Nitzan. "Persistence of Gaussian stationary processes: A spectral perspective." Ann. Probab. 49 (3) 1067 - 1096, May 2021. https://doi.org/10.1214/20-AOP1470

Information

Received: 1 October 2019; Revised: 1 July 2020; Published: May 2021
First available in Project Euclid: 7 April 2021

Digital Object Identifier: 10.1214/20-AOP1470

Subjects:
Primary: 42A38, 60G10, 60G15

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • May 2021
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