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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 3, Pages 439–455 (Mi tvp1553)  

This article is cited in 4 scientific papers (total in 4 papers)

Rate of convergence in the SLLN for associated sequences and fields

M. A. Vronskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Inequalities of the Rosenthal type for the moments of sums of associated random variables are specified on the lattice $\mathbb{Z}^d$. By means of the inequalities an estimate of the rate of convergence is obtained in the strong law of large numbers (SLLN) for associated stochastic processes and random fields.

Keywords: random fields, association, inequalities of the Rosenthal type, rate of convergence in SLLN.

DOI: https://doi.org/10.4213/tvp1553

Full text: PDF file (714 kB)

English version:
Theory of Probability and its Applications, 1999, 43:3, 449–462

Bibliographic databases:

Received: 21.04.1997

Citation: M. A. Vronskii, “Rate of convergence in the SLLN for associated sequences and fields”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 439–455; Theory Probab. Appl., 43:3 (1999), 449–462

Citation in format AMSBIB
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\by M.~A.~Vronskii
\paper Rate of convergence in the SLLN for associated sequences and fields
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 3
\pages 439--455
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\zmath{https://zbmath.org/?q=an:0951.60026}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 449--462
\crossref{https://doi.org/10.1137/S0040585X97976994}
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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. Bakhtin Y.Y., “A functional central limit theorem for transformed solutions to the multidimensional Burgers equation with random initial data”, Doklady Mathematics, 61:3 (2000), 417–419  mathscinet  zmath  isi
    2. N. Yu. Kryzhanovskaya, “Moment Inequality for Sums of Multi-Indexed Dependent Random Variables”, Math. Notes, 83:6 (2008), 770–782  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Xing G.-d., Yang Sh.-ch., “A Note on the Convergence Rate of Strong Law of Large Numbers for Positively Associated Sequences”, Commun. Stat.-Theory Methods, 41:6 (2012), 1116–1125  crossref  mathscinet  zmath  isi  elib  scopus
    4. Xing G.-D., Yang Sh.-Ch., “Rate of Convergence of Strong Law of Large Numbers For Positively Associated Sequences”, Commun. Stat.-Theory Methods, 43:13 (2014), 2752–2765  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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