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A new proof of an old result by Pickands
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J.M.P. Albin, Chalmers University of Technology, Sweden
Hyemi Choi, Chonbuk National University, Korea
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Abstract
Let {ξ(t)}t∈ [0,h] be a stationary
Gaussian process with covariance function r such that r(t)
=1-C|t|α +o(|t|α) as t→0. We give a new and direct
proof of a result originally obtained by Pickands,
on the asymptotic behaviour as u → ∞ of the
probability P{supt ∈ [0,h] ξ(t)>u } that the process ξ
exceeds the level u . As a by-product, we obtain a new
expression for Pickands constant Hα.
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Full text: PDF
Pages: 339-345
Published on: September 12, 2010
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Electronic Communications in Probability. ISSN: 1083-589X |
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