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On long-range dependence of random measures

Published online by Cambridge University Press:  11 January 2017

Daniel Vašata
Affiliation:
Czech Technical University in Prague
Corresponding
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Abstract

This paper deals with long-range dependence of random measures on ℝ d . By examples, it is demonstrated that one must be careful in order to define it consistently. Therefore, we define long-range dependence by a rather specific second-order condition and provide an equivalent formulation involving the asymptotic behaviour of the Bartlett spectrum near the origin. Then it is shown that the defining condition may be formulated less strictly when the additional isotropy assumption holds. Finally, we present an example of a long-range dependent random measure based on the 0-level excursion set of a Gaussian random field for which the corresponding spectral density and its asymptotics are explicitly derived.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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