Abstract
In this paper, we present a duality relationship between regular conditional free energy and regular conditional relative entropy given a sub-s-algebra. This is achieved by using a relation between the Radon-Nikodym derivative of probability measures and that of regular conditional probability measures. Some properties of the regular conditional relative entropy under consideration are also given. The duality relation can be applied in a finite horizon robust state estimation problem for finite-alphabet hidden Markov models.
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