The problem of estimating a finite state Markov chain observed via a process on the same state space is discussed. Optimal solutions are given for both the ``weak'' and ``strong'' formulations of the problem. The ``weak'' formulation proceeds using a reference probability and a measure change for the Markov chain. The ``strong'' formulation considers an observation process related to perturbations of the counting processes associated with the Markov chain. In this case the ``small noise'' convergence is investigated.
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2074
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