{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T05:03:01Z","timestamp":1791176581868,"version":"4.1.0"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2005,5,24]],"date-time":"2005-05-24T00:00:00Z","timestamp":1116892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Centre for Mathematical Physics"},{"DOI":"10.13039\/501100001732","name":"Danish National Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001732","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Community's \u2018Human potential programme\u2019","award":["HPRN-CT-2000-00100"],"award-info":[{"award-number":["HPRN-CT-2000-00100"]}]},{"DOI":"10.13039\/100008395","name":"Danish Social Science Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008395","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator does not exist, an estimator can be obtained by using a penalized likelihood function or by the Markov chain Monte Carlo procedure with a suitable prior. The methodology and its implementation are illustrated by examples and simulation studies.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2005.00508.x","type":"journal-article","created":{"date-parts":[[2005,5,24]],"date-time":"2005-05-24T23:30:01Z","timestamp":1116977401000},"page":"395-410","source":"Crossref","is-referenced-by-count":105,"title":["Statistical Inference for Discretely Observed Markov Jump Processes"],"prefix":"10.1093","volume":"67","author":[{"given":"Mogens","family":"Bladt","sequence":"first","affiliation":[{"name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico , M\u00e9xico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"S\u00f8rensen","sequence":"additional","affiliation":[{"name":"University of Copenhagen , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2005,5,24]]},"reference":[{"key":"2023040705113610100_","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/1468-0262.00274","article-title":"Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach","volume":"70","author":"A\u00eft-Sahalia","year":"2002","journal-title":"Econometrica"},{"key":"2023040705113610100_","volume-title":"Handbook of Financial Econometrics","author":"Bibby","year":"2004"},{"key":"2023040705113610100_","volume-title":"Statistical Inference for Markov Processes","author":"Billingsley","year":"1961"},{"key":"2023040705113610100_","volume-title":"Matrix-analytic Methods: Theory and Applications","author":"Bladt","year":"2002"},{"key":"2023040705113610100_","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1090\/S0002-9939-1966-0202740-6","article-title":"On the existence and uniqueness of the real logarithm of a matrix","volume":"17","author":"Culver","year":"1966","journal-title":"Proc. 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