{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:06Z","timestamp":1753889766729,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,9,4]],"date-time":"2015-09-04T00:00:00Z","timestamp":1441324800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["324432"],"award-info":[{"award-number":["324432"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["257005"],"award-info":[{"award-number":["257005"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The goal of this work is to formally abstract a Markov process evolving in\ndiscrete time over a general state space as a finite-state Markov chain, with\nthe objective of precisely approximating its state probability distribution in\ntime, which allows for its approximate, faster computation by that of the\nMarkov chain. The approach is based on formal abstractions and employs an\narbitrary finite partition of the state space of the Markov process, and the\ncomputation of average transition probabilities between partition sets. The\nabstraction technique is formal, in that it comes with guarantees on the\nintroduced approximation that depend on the diameters of the partitions: as\nsuch, they can be tuned at will. Further in the case of Markov processes with\nunbounded state spaces, a procedure for precisely truncating the state space\nwithin a compact set is provided, together with an error bound that depends on\nthe asymptotic properties of the transition kernel of the original process. The\noverall abstraction algorithm, which practically hinges on piecewise constant\napproximations of the density functions of the Markov process, is extended to\nhigher-order function approximations: these can lead to improved error bounds\nand associated lower computational requirements. The approach is practically\ntested to compute probabilistic invariance of the Markov process under study,\nand is compared to a known alternative approach from the literature.<\/jats:p>","DOI":"10.2168\/lmcs-11(3:8)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:02Z","timestamp":1479735962000},"source":"Crossref","is-referenced-by-count":9,"title":["Quantitative Approximation of the Probability Distribution of a Markov Process by Formal Abstractions"],"prefix":"10.46298","volume":"Volume 11, Issue 3","author":[{"given":"Sadegh Esmaeil Zadeh","family":"Soudjani","sequence":"first","affiliation":[]},{"given":"Alessandro","family":"Abate","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,9,4]]},"reference":[{"key":"1092:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1584\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1584\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:07:09Z","timestamp":1681243629000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1584"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,4]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(3:8)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1504.00039","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1504.00039","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"doi","id":"10.1007\/978-3-030-30281-8_19","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,9,4]]},"article-number":"1584"}}