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An asymptotic formula for the Bayes risk in discriminating between two Markov chains

Part of: Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

A. V. Nagaev
A. V. Nagaev*
Affiliation:
Nicolaus Copernicus University, Toruń
*
1Postal address: Faculty of Mathematics and Informatics, Nicolaus Copernicus University, Toruń, Poland. Email: [email protected]
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Abstract

The problem of discriminating between two Markov chains is considered. It is assumed that the common state space of the chains is finite and all the finite dimensional distributions are mutually absolutely continuous. The Bayes risk is expressed through large deviation probabilities for sums of random variables defined on an auxiliary Markov chain. The proofs are based on a large deviation theorem recently established by Z. Szewczak.

Keywords

Cramér large deviationsPerron–Frobenius theoremlikelihood ratioprimitive matrixspectral radius

MSC classification

Primary: 62M02: Markov processes
Secondary: 60F10: Large deviations
Type
Estimation problems
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 131 - 141
Copyright
Copyright © Applied Probability Trust 2001 

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References

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