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

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 .
nonlinear filtering; piecewise-deterministic Markov processes; optimal stopping
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/705922
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