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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 109–125 (Mi tvp238)  

This article is cited in 3 scientific papers (total in 3 papers)

Central limit theorems in Hölder topologies for Banach space valued random fields

A. Račkauskasa, Ch. Suquetb

a The Faculty of Mathematics and Informatics, Vilnius University
b University of Sciences and Technologies

Abstract: For rather general moduli of smoothness $\rho$, such as $\rho(h)=h^\alpha \log^\beta (c/h)$, we consider the Hölder spaces $H_{\rho}(B)$ of functions $[0,1]^d \to B$, where $B$ is a separable Banach space. Using isomorphism between $H_{\rho}(B)$ and some sequence Banach space we follow a very natural way to study, in terms of second differences, the central limit theorem for independent identically distributed sequences of random elements in $H_{\rho}(B)$.

Keywords: Banach valued Brownian motion, central limit theorem, Rosenthal inequality, Schauder decomposition, second difference, skew pyramidal basis, tightness, type 2 space.

DOI: https://doi.org/10.4213/tvp238

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English version:
Theory of Probability and its Applications, 2005, 49:1, 77–92

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Received: 15.05.2001
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Citation: A. Račkauskas, Ch. Suquet, “Central limit theorems in Hölder topologies for Banach space valued random fields”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 109–125; Theory Probab. Appl., 49:1 (2005), 77–92

Citation in format AMSBIB
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\pages 109--125
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\transl
\jour Theory Probab. Appl.
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\pages 77--92
\crossref{https://doi.org/10.1137/S0040585X97980889}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Račkauskas A., Suquet Ch., Zemlys V., “A Hölderian functional central limit theorem for a multi-indexed summation process”, Stochastic Process. Appl., 117:8 (2007), 1137–1164  crossref  mathscinet  zmath  isi  scopus
    2. Zemlys V., “A Hölderian FCLT for some multiparameter summation process of independent non–identically distributed random variables”, Electron. J. Probab., 13 (2008), 2259–2282  crossref  mathscinet  zmath  isi  scopus
    3. Račkauskas A., Suquet Ch., “Hölderian invariance principle for Hilbertian linear processes”, ESAIM Probab. Stat., 13 (2009), 261–275  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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