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January, 1993 Identifying a Large Deviation Rate Function
I. H. Dinwoodie
Ann. Probab. 21(1): 216-231 (January, 1993). DOI: 10.1214/aop/1176989402


Assume a sequence of probabilities $\{P_n\}$ has a large deviation rate function $I$. It is proved that $I$ takes a form analogous to a convex conjugate. If $I$ is also assumed convex, then $I$ is a convex conjugate of an explicitly defined function $\psi$. The results are applied to the empirical law of a Markov chain yielding universal bounds on $I$. Examples are given of Markov chains in which the empirical law has a large deviation rate strictly between the given bounds.


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I. H. Dinwoodie. "Identifying a Large Deviation Rate Function." Ann. Probab. 21 (1) 216 - 231, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0777.60024
MathSciNet: MR1207224
Digital Object Identifier: 10.1214/aop/1176989402

Primary: 60F10

Keywords: large deviations , Markov chain

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • January, 1993
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