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Nonstationarity in ℝn is second-order stationarity in ℝ2n

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Olivier Perrin  and
Wendy Meiring
Olivier Perrin*
Affiliation:
Université Toulouse 1
Wendy Meiring*
Affiliation:
University of California, Santa Barbara
*
∗Postal address: GREMAQ, Université Toulouse 1, 21, Allée de Brienne, 31000 Toulouse, France. Email address: perrin@cict.fr
∗∗Postal address: Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
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Abstract

We prove that a nonstationary random field indexed by ℝn with moments at least of order 2 can always be viewed as second-order stationary in ℝ2n.

Keywords

Nonstationaritybijective transformationsecond-order stationarity

MSC classification

Primary: 60G60: Random fields
Secondary: 60G12: General second-order processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 815 - 820
Copyright
Copyright © Applied Probability Trust 2003 

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