International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 801303, 23 pages
http://dx.doi.org/10.1155/2011/801303
Research Article

Blackwell Spaces and 𝜖 -Approximations of Markov Chains

Giacomo Aletti1 and Diane Saada2

1ADAMSS Centre (ex MIRIAM) and Department of Mathematics, University of Milan, Via Saldini 50, 20133 Milan, Italy
2Department of Statistics, The Hebrew University of Jerusalem, Jerusalem 91905, Israel

Received 31 December 2010; Revised 11 April 2011; Accepted 24 May 2011

Academic Editor: Michel Benaïm

Copyright © 2011 Giacomo Aletti and Diane Saada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics.