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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 2, Pages 292–311
DOI: https://doi.org/10.4213/tvp108 (Mi tvp108) 		 
This article is cited in 3 scientific papers (total in 3 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
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DOI: https://doi.org/10.4213/tvp108
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.
Received: 08.02.2001
Revised: 15.10.2003
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 2, Pages 248–264
DOI: https://doi.org/10.1137/S0040585X97981652
Bibliographic databases:
Language: Russian
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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  • https://www.mathnet.ru/eng/tvp/v50/i2/p292
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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