Geodesic
The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 292-311

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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, orthonormal basis, Schoenberg representation, equivalent Gaussian measures, regular operators, almost everywhere convergence.
Mots-clés : conditional distributions 
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     author = {S. Ya. Shatskikh},
     title = {The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {292--311},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a4/}
}
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S. Ya. Shatskikh. The strong law of large numbers for triangular array scheme of conditional distributions of stable elliptically contoured measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 292-311. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a4/