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Matematicheskie Trudy, 1999, Volume 2, Number 1, Pages 140–159 (Mi mt149)  

Central Limit Theorem in the Space of Continuous Functions in the Case of Convergence to a Stable Distribution

E. I. Ostrovskii

Obninsk Institute for Nuclear Power Engineering
Abstract: In this article we study weak convergence of distributions of normed sums of independent random fields with an arbitrary compact parametric set to a nondegenerate stable distribution in the corresponding Banach space of continuous functions. We present new entropy conditions for the parametric set which provide this convergence.
Key words: Pisier functional, entropy weak convergence, stable distribution, nonasymptotic estimate.
Received: 28.07.1998
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: E. I. Ostrovskii, “Central Limit Theorem in the Space of Continuous Functions in the Case of Convergence to a Stable Distribution”, Mat. Tr., 2:1 (1999), 140–159; Siberian Adv. Math., 9:3 (1999), 132–150
Citation in format AMSBIB
\Bibitem{Ost99}
\by E.~I.~Ostrovskii
\paper Central Limit Theorem in the~Space of Continuous Functions in the~Case of Convergence to a~Stable Distribution
\jour Mat. Tr.
\yr 1999
\vol 2
\issue 1
\pages 140--159
\mathnet{http://mi.mathnet.ru/mt149}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1762622}
\zmath{https://zbmath.org/?q=an:0954.60015|0932.60021}
\transl
\jour Siberian Adv. Math.
\yr 1999
\vol 9
\issue 3
\pages 132--150
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