Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set and let Y be defined by Y_t = h(X_t ), (t ≥ 0). We address the filtering problem for X in terms of the observation Y, which is not directly affected by noise. We write down explicit equations for the filtering process. We show that it is a Markov process with the Feller property. We also prove that it is a piecewise-deterministic Markov process in the sense of Davis, and we identify its characteristics explicitly. We finally solve an optimal stopping problem for X with partial observation, i.e. where the moment of stopping is required to be a stopping time with respect to the natural filtration of Y .
Filtering of continuous-time Markov chains with noise-free observation and applications
CONFORTOLA, FULVIA;
2013-01-01
Abstract
Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set and let Y be defined by Y_t = h(X_t ), (t ≥ 0). We address the filtering problem for X in terms of the observation Y, which is not directly affected by noise. We write down explicit equations for the filtering process. We show that it is a Markov process with the Feller property. We also prove that it is a piecewise-deterministic Markov process in the sense of Davis, and we identify its characteristics explicitly. We finally solve an optimal stopping problem for X with partial observation, i.e. where the moment of stopping is required to be a stopping time with respect to the natural filtration of Y .File | Dimensione | Formato | |
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