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Central limit theorem for wave-functionals of Gaussian processes

Part of: Stochastic processes Special processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Vladimir Piterbarg  and
Igor Rychlik
Vladimir Piterbarg*
Affiliation:
Moscow University
Igor Rychlik*
Affiliation:
University of Lund
*
∗ Postal address: Faculty of Mechanics and Mathematics, Moscow University, Vorobyovy Gory, Moscow 119 899, Russia.
∗∗ Postal address: Centre for Mathematical Sciences, University of Lund, Box 118, S-22100 Lund, Sweden. Email address: [email protected]
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Abstract

In this paper a central limit theorem is proved for wave-functionals defined as the sums of wave amplitudes observed in sample paths of stationary continuously differentiable Gaussian processes. Examples illustrating this theory are given.

Keywords

CrossingsSlepian modelsstrong mixing propertycentral limit theorem

MSC classification

Primary: 60G15: Gaussian processes 60G35: Signal detection and filtering
Secondary: 60K40: Other physical applications of random processes 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 158 - 177
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Supported by Swedish Research Council for Engineering Sciences grant 908911 TFR 91-747.

Supported in part by Office of Naval Research under Grant N00014-93-1-0841.

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