High Excursions of a Quadratic form for a Gaussian Stationary Vector Process

High Excursions of a Quadratic form for a Gaussian Stationary Vector Process

Exact asymptotic behavior is given for high excursion probabilities of a quadratic form for a zero-mean Gaussian stationary vector process with Pickands’ type covariance matrix in the vicinity of zero. The case of a quadratic form with a positive maximum eigenvalue of order 1 is considered.

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-04, Vol.262 (4), p.476-492
1. Verfasser: Zhdanov, A. I.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Covariance matrix
Eigenvalues
Gaussian process
Mathematical analysis
Mathematics
Mathematics and Statistics
Quadratic forms
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Beschreibung
Zusammenfassung:Exact asymptotic behavior is given for high excursion probabilities of a quadratic form for a zero-mean Gaussian stationary vector process with Pickands’ type covariance matrix in the vicinity of zero. The case of a quadratic form with a positive maximum eigenvalue of order 1 is considered.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05829-5