PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

Naomi Feldheim*, Ohad Feldheim, Shahaf Nitzan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageAmerican English
Pages (from-to)1067-1096
Number of pages30
JournalAnnals of Probability
Volume49
Issue number3
DOIs
StatePublished - May 2021

Bibliographical note

Funding Information:
Acknowledgments. N.F. acknowledges the supports of NSF postdoctoral fellowship MSPRF-1503094 held at Stanford. O.F. acknowledges the support of NSF grant DMS-1613091 while holding a postdoctoral position at Stanford. S.N. acknowledges the support of NSF Grant DMS-1600726.

Publisher Copyright:
© Institute of Mathematical Statistics, 2021

Keywords

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

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