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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 3, Pages 602–616
DOI: https://doi.org/10.4213/tvp5251 (Mi tvp5251) 		 
On the sub-Gaussianity of the $r$-correlograms

R. Giulianoa, M. Ordóñez Cabrerab, A. Volodinc

a Dipartimento di Matematica, Università di Pisa, Italy
b Departamento Análisis Matemático, Universidad de Sevilla, Spain
c Department of Mathematics and Statistics, University of Regina, Canada
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DOI: https://doi.org/10.4213/tvp5251
Abstract: In this article, we show that the centered relay correlation function is a sub-Gaussian random variable. This is done by a careful analysis of its Laplace transform and by estimating the sub-Gaussian standard of the $r$-correlograms.
Keywords: relay correlogram function, sub-Gaussian random variables, sub-Gaussian standard, Laplace transform, stationary Gaussian process.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 1.13556.2019/13.1
Ministerio de Educación y Ciencia, Spain MTM2015-65242-C2-1-P
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía P08-FQM-03543
Istituto Nazionale di Alta Matematica "Francesco Severi"
Fondi di Ateneo
The first listed author acknowledges was supported by the University of Pisa (Fondi di Ateneo). A part of research of A. Volodin has been done during the visit to the University of Pisa in December 2016. The authors would like to express their appreciation to the INDAM for supporting this visit. The research was supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project № 1.13556.2019/13.1. The research of M. Ordóñez Cabrera was partially supported by the Plan Andaluz de Investigacion de la Junta de Andalucia FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P.
Received: 26.09.2018
Revised: 23.02.2020
Accepted: 27.02.2020
English version:
Theory of Probability and its Applications, 2020, Volume 65, Issue 3, Pages 470–481
DOI: https://doi.org/10.1137/S0040585X97T99006X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. Giuliano, M. Ordóñez Cabrera, A. Volodin, “On the sub-Gaussianity of the $r$-correlograms”, Teor. Veroyatnost. i Primenen., 65:3 (2020), 602–616; Theory Probab. Appl., 65:3 (2020), 470–481
Citation in format AMSBIB
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\paper On the sub-Gaussianity of the $r$-correlograms
\jour Teor. Veroyatnost. i Primenen.
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\vol 65
\issue 3
\pages 602--616
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\crossref{https://doi.org/10.4213/tvp5251}
\transl
\jour Theory Probab. Appl.
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\pages 470--481
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