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December 2016 On long-range dependence of random measures
Daniel Vašata
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Adv. in Appl. Probab. 48(4): 1235-1255 (December 2016).

Abstract

This paper deals with long-range dependence of random measures on ℝd. 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.

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Daniel Vašata. "On long-range dependence of random measures." Adv. in Appl. Probab. 48 (4) 1235 - 1255, December 2016.

Information

Published: December 2016
First available in Project Euclid: 24 December 2016

zbMATH: 1384.60083
MathSciNet: MR3595773

Subjects:
Primary: 60D05
Secondary: 52A40

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 4 • December 2016
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