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Hidden Markov ProcessesTheory and Applications to Biology$
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M. Vidyasagar

Print publication date: 2014

Print ISBN-13: 9780691133157

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691133157.001.0001

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Introduction to Large Deviation Theory

Introduction to Large Deviation Theory

(p.129) Chapter Five Introduction to Large Deviation Theory
Hidden Markov Processes

M. Vidyasagar

Princeton University Press

This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct an empirical distribution. It then considers the notion of a lower semi-continuous function and that of a lower semi-continuous relaxation before discussing the large deviation property for i.i.d. samples. In particular, it describes Sanov's theorem for a finite alphabet and proceeds by analyzing large deviation property for Markov chains, taking into account stationary distributions, entropy and relative entropy rates, the rate function for doubleton frequencies, and the rate function for singleton frequencies.

Keywords:   large deviation theory, probability distribution, lower semi-continuous function, lower semi-continuous relaxation, large deviation property, Sanov's theorem, Markov chain, stationary distribution, relative entropy rate, rate function

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