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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21592

Barbour, A D; Lindvall, T (2006). Translated Poisson approximation for Markov chains. Journal of Theoretical Probability, 19(3):609-630.

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Abstract

The paper is concerned with approximating the distribution of a sum W of integer valued random variables Y i , 1 ≤ i ≤ n, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson distribution, with mean and variance chosen to be close to those of W, and the error is measured with respect to the total variation norm. Error bounds comparable to those found for normal approximation with respect to the weaker Kolmogorov distance are established, provided that the distribution of the sum of the Y i ’s between the successive visits of X to a reference state is aperiodic. Without this assumption, approximation in total variation cannot be expected to be good.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:2006
Deposited On:05 Jan 2010 15:25
Last Modified:27 Nov 2013 16:56
Publisher:Springer
ISSN:0894-9840
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/s10959-006-0047-9
Related URLs:http://arxiv.org/abs/0810.0599
Citations:Web of Science®. Times Cited: 7
Google Scholar™
Scopus®. Citation Count: 10

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