High excursions of a quadratic form for a Gaussian stationary vector process

A. I. Zhdanov

Lomonosov Moscow State University, Moscow, Russia

Abstract: 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.

UDC: 519.21

 English version: Journal of Mathematical Sciences (New York), 2022, 262:4, 476–492