A Duality Relationship for Regular Conditional Relative Entropy

Authors:	Petersen Ian, University of NSW at ADFA, Australia Xie Li, Chinese University of Hong Kong, Hong Kong Ugrinovskii Valery, University of NSW at ADFA, Australia
Topic:	1.4 Stochastic Systems
Session:	Modeling and Estimation of Stochastic Systems
Keywords:	Duality relationship, Radon-Nikodymderivative, regular conditional probability measure, regular conditional relative entropy

Abstract

In this paper, we present a duality relationship between regularconditional free energy and regular conditional relative entropygiven a sub-sigma-algebra. This is achieved by using a relation between the Radon-Nikodymderivative of probability measures and that of regular conditionalprobability measures. Some properties of the regular conditionalrelative entropy under consideration are also given. The dualityrelation can be applied in a finite horizon robust stateestimation problem for finite-alphabet hidden Markov models.