Extremes of independent Gaussian processes |
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Authors: | Zakhar Kabluchko |
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Institution: | (1) Institute of Problems of Mechanical Engineering (Russian Academy of Science), St. Petersburg, Russia; |
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Abstract: | For every n ∈ ℕ, let X
1n
,..., X
nn
be independent copies of a zero-mean Gaussian process X
n
= {X
n
(t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process a
n
(M
n
− b
n
), where M
n
(t) = max
i = 1,...,n
X
in
(t), and a
n
, b
n
are normalizing constants. We also provide an analogous characterization for the limits of the process a
n
L
n
, where L
n
(t) = min
i = 1,...,n
|X
in
(t)|. |
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Keywords: | |
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