Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits

Sandra Fortini; Lucia Ladelli; Eugenio Regazzini

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 3, page 515-542
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Fortini, Sandra, Ladelli, Lucia, and Regazzini, Eugenio. "Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits." Bollettino dell'Unione Matematica Italiana 5.3 (2012): 515-542. <http://eudml.org/doc/290847>.

@article{Fortini2012,
abstract = {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.},
author = {Fortini, Sandra, Ladelli, Lucia, Regazzini, Eugenio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {515-542},
publisher = {Unione Matematica Italiana},
title = {Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits},
url = {http://eudml.org/doc/290847},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Fortini, Sandra
AU - Ladelli, Lucia
AU - Regazzini, Eugenio
TI - Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/10//
PB - Unione Matematica Italiana
VL - 5
IS - 3
SP - 515
EP - 542
AB - 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.
LA - eng
UR - http://eudml.org/doc/290847
ER -

References

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