Long gaps between sign-changes of Gaussian stationary processes

Naomi D. Feldheim; Ohad N. Feldheim

doi:10.1093/imrn/rnu020

Long gaps between sign-changes of Gaussian stationary processes

Naomi D. Feldheim, Ohad N. Feldheim

Institute for Mathematics and its Applications

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Abstract

We study the probability of a real-valued stationary process to be positive on a large interval [0, N]. We show that if in some neighborhood of the origin the spectral measure of the process has density which is bounded away from zero and infinity, then the decay of this probability is bounded between two exponential functions in N. This generalizes similar bounds obtained for particular cases, such as a recent result by Antezana, Buckley, Marzo, Olsen.

Original language	English (US)
Pages (from-to)	3021-3034
Number of pages	14
Journal	International Mathematics Research Notices
Volume	2015
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnu020
State	Published - 2015

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© The Author(s) 2014. Published by Oxford University Press. All rights reserved.

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Long gaps between sign-changes of Gaussian stationary processes

Abstract

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