Filtering of continuous-time Markov chains with noise-free observation\n and applications

2010/09/06 by Fulvia Confortola, Confortola, Fulvia, Marco Fuhrman +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G35 #60G40 #60J27 #93E11 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Petri Nets in System Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1009.1039

openalex publication_date 2010/09/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let X be a continuous-time Markov chain in a finite set I, let h be a mapping\nof I onto another set, and let Y be defined by Y_t=h(X_t), (for t nonnegative).\nWe address the filtering problem for X in terms of the observation Y, which is\nnot directly affected by noise. We write down explicit equations for the\nfiltering process and show that this is a Markov process with the Feller\nproperty. We also prove that it is a piecewise-deterministic Markov process in\nthe sense of Davis, and we identify its characteristics explicitly. We finally\nsolve an optimal stopping problem for X with partial observation, i.e. where\nthe moment of stopping is required to be a stopping time with respect to the\nnatural filtration of Y.\n

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