Length of stationary Gaussian excursions

Arijit Chakrabarty, Manish Pandey, Sukrit Chakrabarty

Research output: Contribution to journalArticleAcademicpeer-review


Given that a stationary Gaussian process is above a high threshold, the length of time it spends before going below that threshold is studied. The asymptotic order is determined by the smoothness of the sample paths, which in turn is a function of the tails of the spectral measure. Two disjoint regimes are studied – one in which the second spectral moment is finite and the other in which the tails of the spectral measure are regularly varying and the second moment is infinite.
Original languageEnglish
Pages (from-to)1339-1348
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number3
Early online date9 Dec 2022
Publication statusPublished - 1 Mar 2023


Received by the editors December 1, 2021, and, in revised form, July 19, 2022. 2020 Mathematics Subject Classification. Primary 60G15; Secondary 60G70. Key words and phrases. Gaussian process, high excursions, length of excursion, regular variation. The research of the third author was supported by the NBHM postdoctoral fellowship.

FundersFunder number
National Board for Higher Mathematics


    • Gaussian process
    • high excursions
    • length of excursion
    • regular variation


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