Geodesic
Some results of stable convergence for exchangeable random variables in Hilbert spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 395-403

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Some results of stable convergence for triangular arrays of finitely exchangeable Hilbert-valued random variables are proved. These results, obtained without any integrability hypothesis, complete the classical central limit results. A Berry–Esseen type estimate for their rate of convergence is also given.
Keywords: exchangeable random variables, central limit theorem in Hilbert spaces, rate of convergence, Berry–Esseen type estimate.
Mots-clés : stable convergence 
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     author = {M. E. Mancino and L. Pratelli},
     title = {Some results of stable convergence for exchangeable random variables in {Hilbert} spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {395--403},
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     volume = {45},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a13/}
}
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M. E. Mancino; L. Pratelli. Some results of stable convergence for exchangeable random variables in Hilbert spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 395-403. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a13/