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Content available remote Pickands–Piterbarg Constants for Self-Similar Gaussian Processes
EN
For a centered self-similar Gaussian process {Y (t) : t ∈ [0;∞)} and R≥0 we analyze the asymptotic behavior of [formula], for suitably chosen γ> 0. Additionally, we find bounds for HRY , R > 0, and a surprising relation between HY and the classical Pickands constants.
2
Content available remote Extremes of chi-square processes with trend
EN
This paper studies the supremum of chi-square processes with trend over a threshold-dependent-time horizon. Under the assumptions that the chi-square process is generated from a centered self-similar Gaussian process and the trend function is modeled by a polynomial function, we obtain the exact tail asymptotics of the supremum of the chi-square proces with trend. These results are of interest in applications in engineering, insurance, queueing and statistics, etc. Some possible extensions of our results are also discussed.
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