{"id":"https://openalex.org/W4245774986","doi":"https://doi.org/10.1017/s0021900200012882","title":"Discounted Continuous-Time Controlled Markov Chains: Convergence of Control Models","display_name":"Discounted Continuous-Time Controlled Markov Chains: Convergence of Control Models","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W4245774986","doi":"https://doi.org/10.1017/s0021900200012882"},"language":"en","primary_location":{"id":"doi:10.1017/s0021900200012882","is_oa":false,"landing_page_url":"http://doi.org/10.1017/s0021900200012882","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002012512","display_name":"Tom\u00e1s Prieto-Rumeau","orcid":"https://orcid.org/0000-0003-4677-4725"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tom\u00e1s Prieto-Rumeau","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060670677","display_name":"On\u00e9simo Hern\u00e1ndez\u2013Lerma","orcid":"https://orcid.org/0000-0003-3308-5218"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"On\u00e9simo Hern\u00e1ndez-Lerma","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002012512"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30360621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"04","first_page":"1072","last_page":"1090"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9670000076293945,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9670000076293945,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9595999717712402,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9316999912261963,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8363522291183472},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7565427422523499},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6830517053604126},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6288353204727173},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5708451271057129},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5450539588928223},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4950050711631775},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4861904978752136},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.48290491104125977},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4517280161380768},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44675421714782715},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43340760469436646},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42688286304473877},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.42373979091644287},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4218481183052063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20667722821235657},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12718361616134644},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12507790327072144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10978084802627563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8363522291183472},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7565427422523499},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6830517053604126},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6288353204727173},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5708451271057129},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5450539588928223},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4950050711631775},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4861904978752136},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.48290491104125977},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4517280161380768},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44675421714782715},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43340760469436646},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42688286304473877},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.42373979091644287},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4218481183052063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20667722821235657},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12718361616134644},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12507790327072144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10978084802627563},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0021900200012882","is_oa":false,"landing_page_url":"http://doi.org/10.1017/s0021900200012882","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1980329955","https://openalex.org/W1984006577","https://openalex.org/W1985929135","https://openalex.org/W1994602702","https://openalex.org/W2046624619","https://openalex.org/W2052851812","https://openalex.org/W2124821240","https://openalex.org/W2128670912","https://openalex.org/W2149148771","https://openalex.org/W2150301222"],"related_works":["https://openalex.org/W2943897807","https://openalex.org/W3120484221","https://openalex.org/W4366198066","https://openalex.org/W3047748938","https://openalex.org/W2358522863","https://openalex.org/W4386034604","https://openalex.org/W278441094","https://openalex.org/W3099285423","https://openalex.org/W4381248241","https://openalex.org/W2336173978"],"abstract_inverted_index":{"We":[0,104],"are":[1],"interested":[2],"in":[3],"continuous-time,":[4],"denumerable":[5],"state":[6],"controlled":[7,99],"Markov":[8],"chains":[9],"(CMCs),":[10],"with":[11,102],"compact":[12],"Borel":[13],"action":[14],"sets,":[15],"and":[16,20,59,76,95],"possibly":[17],"unbounded":[18],"transition":[19],"reward":[21,26,58,94],"rates,":[22],"under":[23],"the":[24,55,81,92,106],"discounted":[25],"optimality":[27],"criterion.":[28],"For":[29],"such":[30],"CMCs,":[31],"we":[32,72],"propose":[33,73],"a":[34,37,47,74,98],"definition":[35],"of":[36,39,61,67,80,97],"sequence":[38],"control":[40,49,83],"models":[41],"{\u2133":[42],"n":[43,63],"}":[44],"converging":[45],"to":[46,65],"given":[48],"model":[50,84],"\u2133,":[51,85],"which":[52,86],"ensures":[53],"that":[54],"discount":[56],"optimal":[57,93],"policies":[60],"\u2133":[62],"converge":[64],"those":[66],"\u2133.":[68],"As":[69],"an":[70],"application,":[71],"finite-state":[75],"finite-action":[77],"truncation":[78],"technique":[79],"original":[82],"is":[87],"illustrated":[88],"by":[89],"approximating":[90],"numerically":[91],"policy":[96],"population":[100],"system":[101],"catastrophes.":[103],"study":[105],"corresponding":[107],"convergence":[108],"rates.":[109]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}