Xie, LiUgrinovskii, Valery A.Petersen, Ian R.2026-07-022026-07-022405-8971ORCID:/0000-0003-4856-9450/work/219057271https://hdl.handle.net/1885/733812257In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.This work was supported by the Australian Research Council.6enPublisher Copyright: Copyright © IFAC 2004.a posteriori probability distancesfinite-alphabet hidden Markov modelsregular conditional relative entropy200410.1016/s1474-6670(17)30540-285178326046