Abstract:
Stationary quasi-associated random fields with continuous covariance function are considered. Recently Bulinski, Spodarev, and Timmermann proved a central limit theorem for the excursion set volumes of such random fields. We establish a functional version of this theorem.
Key words and phrases:
excursion sets, quasi-association, functional limit theorem.
Citation:
V. P. Demichev, “Functional central limit theorem for excursion set volumes of quasi-associated random fields”, Probability and statistics. Part 19, Zap. Nauchn. Sem. POMI, 412, POMI, St. Petersburg, 2013, 109–120; J. Math. Sci. (N. Y.), 204:1 (2015), 69–77
\Bibitem{Dem13}
\by V.~P.~Demichev
\paper Functional central limit theorem for excursion set volumes of quasi-associated random fields
\inbook Probability and statistics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 412
\pages 109--120
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5643}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073540}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 1
\pages 69--77
\crossref{https://doi.org/10.1007/s10958-014-2187-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925506095}
Linking options:
https://www.mathnet.ru/eng/znsl5643
https://www.mathnet.ru/eng/znsl/v412/p109
This publication is cited in the following 2 articles:
Andriy Olenko, Dareen Omari, “Reduction Principle for Functionals of Vector Random Fields”, Methodol Comput Appl Probab, 22:2 (2020), 573
Andriy Olenko, Dareen Omari, “Reduction principle for functionals of strong-weak dependent vector random fields”, Braz. J. Probab. Stat., 34:4 (2020)
Citation in format AMSBIB
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