# On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes

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State: Serval

Version: author

State: Serval

Version: author

Serval ID

serval:BIB_0E398DD87431

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes

Journal

Journal of Mathematical Analysis and Applications

ISSN

0022-247X (Print)

Publication state

Published

Issued date

2014

Peer-reviewed

Oui

Volume

409

Number

1

Pages

299-314

Language

english

Abstract

Let {X (t), t >= 0} be a stationary Gaussian process with zero-mean and unit variance. A deep result derived in Piterbarg (2004) [23], which we refer to as Piterbarg's max-discretisation theorem gives the joint asymptotic behaviour (T -> infinity) of the continuous time maximum M(T) = max(t is an element of[0,T]) X(t), and the maximum M-delta(T) = max(t is an element of R(delta)) X(t), with R(delta) subset of [0, T] a uniform grid of points of distance delta = delta(T). Under some asymptotic restrictions on the correlation function Piterbarg's max-discretisation theorem shows that for the limit result it is important to know the speed delta(T) approaches 0 as T -> infinity. The present contribution derives the aforementioned theorem for multivariate stationary Gaussian processes.

Keywords

Gaussian process, Piterbarg discretisation, Limit theorem

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Create date

11/07/2013 6:43

Last modification date

29/03/2017 16:04