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Regular version of the site

Article

On probability of high extremes for product of two independent Gaussian stationary processes

Extremes. 2015. Vol. 18. No. 1. P. 99-108.
Zhdanov A., Piterbarg V.I.

Let X(t), Y(t), t ≥ 0, be two independent zero-mean stationary Gaussian
processes, whose covariance functions are such that ri (t) = 1 − |t|^{a_{i}} + o(|t|^{a_{i}})
as t → 0, with 0 < a_{i} ≤ 2, i = 1, 2 and both of the functions are less than one
for non-zero t . We derive for any p the exact asymptotic behavior of the probability
P(max_{t∈[0,p]}X(t)Y(t) > u) as u → ∞. We discuss possibilities generalizing
obtained results to other Gaussian chaos processes h(X(t)), with a Gaussian vector
process X(t) and a homogeneous function h of positive order.