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June 2011 A central limit theorem and its applications to multicolor randomly reinforced urns
Patrizia Berti, Irene Crimaldi, Luca Pratelli, Pietro Rigo
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J. Appl. Probab. 48(2): 527-546 (June 2011). DOI: 10.1239/jap/1308662642

Abstract

Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = √{(1 / n)∑k=1nXk - E(Xn+1 | Gn)} and Dn = √n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) → N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain √n{(1 / n)∑k=1nX_k - Z} = Cn + DnN(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns.

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Patrizia Berti. Irene Crimaldi. Luca Pratelli. Pietro Rigo. "A central limit theorem and its applications to multicolor randomly reinforced urns." J. Appl. Probab. 48 (2) 527 - 546, June 2011. https://doi.org/10.1239/jap/1308662642

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1225.60038
MathSciNet: MR2840314
Digital Object Identifier: 10.1239/jap/1308662642

Subjects:
Primary: 60B10, 60F05, 60G57, 62F15

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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