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Limit theorems for maxima and crossings of a sequence of Gaussian processes and approximation of random processes

Published online by Cambridge University Press:  14 July 2016

O. V. Seleznjev
O. V. Seleznjev*
Affiliation:
Moscow State University
*
∗Postal address: Faculty of Mathematics and Mechanics, Moscow State University, 117234, Moscow, USSR.
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Abstract

We consider the limit distribution of maxima and point processes, connected with crossings of an increasing level, for a sequence of Gaussian stationary processes. As an application we investigate the limit distribution of the error of approximation of Gaussian stationary periodic processes by random trigonometric polynomials in the uniform metric.

Keywords

MAXIMUM OF GAUSSIAN PROCESSPOINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 17 - 32
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Part of this work was carried out during a visit to the Department of Mathematical Statistics, the University of Lund, Sweden.

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