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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 292–311 (Mi tvp108)  

This article is cited in 2 scientific papers (total in 2 papers)

The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures

S. Ya. Shatskikh

Samara State University

Abstract: This paper deals with conditional distributions of stable elliptically contoured measures on real separable Hilbert space. We consider projections of these measures on an increasing sequence of finite-dimensional linear subspaces spanned by initial elements of orthonormal basis. It is shown that the asymptotic properties of corresponding conditional distributions depends on a choice of a basis of Hilbert space. We give sufficient conditions of a choice of a basis when triangular array schemes of conditional distributions (in a certain sense) obey the strong law of large numbers.

Keywords: stable elliptically contoured measures, conditional distributions, orthonormal basis, Schoenberg representation, equivalent Gaussian measures, regular operators, almost everywhere convergence.

DOI: https://doi.org/10.4213/tvp108

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English version:
Theory of Probability and its Applications, 2006, 50:2, 248–264

Bibliographic databases:

Received: 08.02.2001
Revised: 15.10.2003

Citation: S. Ya. Shatskikh, “The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 292–311; Theory Probab. Appl., 50:2 (2006), 248–264

Citation in format AMSBIB
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\by S.~Ya.~Shatskikh
\paper The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures
\jour Teor. Veroyatnost. i Primenen.
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\pages 292--311
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\zmath{https://zbmath.org/?q=an:1090.60031}
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\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 2
\pages 248--264
\crossref{https://doi.org/10.1137/S0040585X97981652}
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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. E. A. Savinov, “Predelnaya teorema dlya kopul preobrazovanii nezavisimosti $t$-raspredeleniya Styudenta”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 8(89), 69–85  mathnet  elib
    2. E. A. Savinov, “Limit theorem for maximum of random variables with copulas which are IT-copulas of Student’s ${t}$-distribution”, Theory Probab. Appl., 59:3 (2015), 508–516  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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