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Theory of Probability and Mathematical Statistics

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Increasing domain asymptotics for the first Minkowski functional of spherical random fields


Authors: N. N. Leonenko and M. D. Ruiz-Medina
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 127-149
MSC (2010): Primary 60G60, 60F05, 60G10, 62E20
DOI: https://doi.org/10.1090/tpms/1053
Published electronically: February 21, 2019
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Abstract: The restriction to the sphere of a homogeneous and isotropic random field defines a spherical isotropic random field. This paper derives central and noncentral limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in $ \mathbb{R}^{3}$. Both scenarios are motivated by their interesting applications in the analysis of the Cosmic Microwave Background (CMB) radiation.


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Additional Information

N. N. Leonenko
Affiliation: Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, United Kingdom
Email: LeonenkoN@cardiff.ac.uk

M. D. Ruiz-Medina
Affiliation: Department of Statistics and Operations Research, Campus de Fuente Nueva s/n, University of Granada, E-18071 Granada, Spain
Email: mruiz@ugr.es

DOI: https://doi.org/10.1090/tpms/1053
Keywords: Central and noncentral limit theorems, chi-squared random fields, Gaussian random fields, Karhunen--Lo\'eve expansion, spherical Rosenblatt distribution
Received by editor(s): September 17, 2017
Published electronically: February 21, 2019
Additional Notes: The first author was supported in particular by Cardiff Incoming Visiting Fellowship Scheme, International Collaboration Seedcorn Fund, Data Innovation URI Seedcorn Fund, and Australian Research Council’s Discovery Projects funding scheme (project DP160101366).
The authors were supported by project MTM2015-71839-P of MINECO, Spain (co-funded with FEDER funds).
Dedicated: This contribution is dedicated to the 85th anniversary of Professor Mykhailo Yosypovych Yadrenko
Article copyright: © Copyright 2019 American Mathematical Society