PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Naomi Feldheim; Ohad Feldheim; Shahaf Nitzan

doi:10.1214/20-AOP1470

PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Naomi Feldheim
, Ohad Feldheim
, Shahaf Nitzan

Bar-Ilan University, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1067-1096
Number of pages	30
Journal	Annals of Probability
Volume	49
Issue number	3
DOIs	https://doi.org/10.1214/20-AOP1470
State	Published - May 2021

Keywords

Chebyshev polynomials
Gaussian process
gap probability
one-sided barrier
persistence
spectral measure
stationary process

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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Cite this

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title = "PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE",

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.",

keywords = "Chebyshev polynomials, Gaussian process, gap probability, one-sided barrier, persistence, spectral measure, stationary process",

author = "Naomi Feldheim and Ohad Feldheim and Shahaf Nitzan",

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year = "2021",

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T2 - A SPECTRAL PERSPECTIVE

AU - Feldheim, Naomi

AU - Feldheim, Ohad

AU - Nitzan, Shahaf

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2021

PY - 2021/5

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N2 - 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.

AB - 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.

KW - Chebyshev polynomials

KW - Gaussian process

KW - gap probability

KW - one-sided barrier

KW - persistence

KW - spectral measure

KW - stationary process

UR - https://www.scopus.com/pages/publications/85112036990

U2 - 10.1214/20-AOP1470

DO - 10.1214/20-AOP1470

M3 - Article

SN - 0091-1798

VL - 49

SP - 1067

EP - 1096

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Abstract

Keywords

ASJC Scopus subject areas

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