October 2020 Reduction principle for functionals of strong-weak dependent vector random fields
Andriy Olenko, Dareen Omari
Braz. J. Probab. Stat. 34(4): 885-908 (October 2020). DOI: 10.1214/20-BJPS467


We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed distributions. Contrary to the case of scalar long-range dependent random fields, it is shown that the asymptotic behaviour of such functionals is not necessarily determined by the terms at their Hermite rank. The results are illustrated by an application to the first Minkowski functional of the Student random fields. Some simulation studies based on the theoretical findings are also presented.


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Andriy Olenko. Dareen Omari. "Reduction principle for functionals of strong-weak dependent vector random fields." Braz. J. Probab. Stat. 34 (4) 885 - 908, October 2020. https://doi.org/10.1214/20-BJPS467


Received: 1 September 2019; Accepted: 1 February 2020; Published: October 2020
First available in Project Euclid: 25 September 2020

MathSciNet: MR4153648
Digital Object Identifier: 10.1214/20-BJPS467

Keywords: first Minkowski functional , long-range dependence , Non-central limit theorem , Random fields , reduction , Student random fields

Rights: Copyright © 2020 Brazilian Statistical Association


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Vol.34 • No. 4 • October 2020
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