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Asymptotic Normality of Discrete-Time Markov Control Processes

Part of: Limit theorems Markov processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Armando F. Mendoza-Pérez  and
Onésimo Hernández-Lerma
Armando F. Mendoza-Pérez*
Affiliation:
Universidad Politécnica de Chiapas
Onésimo Hernández-Lerma*
Affiliation:
CINVESTAV
*
∗Postal address: Universidad Politécnica de Chiapas, Calle Eduardo J. Selvas S/N, Tuxtla Gutiérrez, Chiapas, Mexico. Email address: mepa680127@hotmail.com
∗∗Postal address: Department of Mathematics, CINVESTAV-IPN, A. Postal 14-740, Mexico DF 07000, Mexico. Email address: ohernand@math.cinvestav.mx
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Abstract

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In this paper we study the asymptotic normality of discrete-time Markov control processes in Borel spaces, with possibly unbounded cost. Under suitable hypotheses, we show that the cost sequence is asymptotically normal. As a special case, we obtain a central limit theorem for (noncontrolled) Markov chains.

Keywords

(Discrete-time) Markov control processaverage cost criteriaaverage varianceasymptotic normality

MSC classification

Secondary: 93E20: Optimal stochastic control 90C40: Markov and semi-Markov decision processes 60F05: Central limit and other weak theorems 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 778 - 795
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Research partially supported by CONACyT grant 104001.

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