Fortini, Sandra and Ladelli, Lucia and Regazzini, Eugenio:
Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.3, p. 515-542, (English)
pdf (417 Kb), djvu (293 Kb). | MR 3051735 | Zbl 1286.60025
Sunto
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws - as limits in law of normed sums in different rows of the array - is emphasized. Necessary and sufficient conditions for convergence to a specific form in the above class of measures are then given. Moreover, sufficient conditions for convergence of sums in a single row are proved. Finally, a potentially useful variant of the formulation of the results just summarized is briefly sketched, a more complete study of it being deferred to a future work.
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