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Hoeffding's inequality for uniformly ergodic Markov chains

โœ Scribed by Peter W. Glynn; Dirk Ormoneit


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
72 KB
Volume
56
Category
Article
ISSN
0167-7152

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โœฆ Synopsis


We provide a generalization of Hoe ding's inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expectation is particularly useful in situations where we require uniform control on the constants appearing in the bound.


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In several papers Meyer, singly and with coauthors, established the usefulness of the group generalized inverse in the study and computations of various aspects of Markov chains. Here we are interested in those results which concern bounds on the condition number of the chain and on the error in the