Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 48, Number 4 (2016), 1235-1255.
On long-range dependence of random measures
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.
Adv. in Appl. Probab., Volume 48, Number 4 (2016), 1235-1255.
First available in Project Euclid: 24 December 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 52A40: Inequalities and extremum problems
Vašata, Daniel. On long-range dependence of random measures. Adv. in Appl. Probab. 48 (2016), no. 4, 1235--1255. https://projecteuclid.org/euclid.aap/1482548436