Long gaps between sign-changes of Gaussian stationary processes

Naomi D. Feldheim, Ohad N. Feldheim

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 languageEnglish
Pages (from-to)3021-3034
Number of pages14
JournalInternational Mathematics Research Notices
Volume2015
Issue number11
DOIs
StatePublished - 2015
Externally publishedYes

Bibliographical note

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

Funding

FundersFunder number
European Research Council

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