{"paper":{"title":"Filtering of continuous-time Markov chains with noise-free observation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fulvia Confortola, Marco Fuhrman","submitted_at":"2010-09-06T12:27:38Z","abstract_excerpt":"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), (for t nonnegative). 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 and show that this 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 observ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1039","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}