{"id":"https://openalex.org/W2948062386","doi":"https://doi.org/10.1137/18m1169151","title":"Representation Formulas for Limit Values of Long Run Stochastic Optimal Controls","display_name":"Representation Formulas for Limit Values of Long Run Stochastic Optimal Controls","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2948062386","doi":"https://doi.org/10.1137/18m1169151","mag":"2948062386"},"language":"en","primary_location":{"id":"doi:10.1137/18m1169151","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169151","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5013262276","display_name":"Rainer Buckdahn","orcid":"https://orcid.org/0000-0002-3968-8012"},"institutions":[{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Rainer Buckdahn","raw_affiliation_strings":["LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)"],"affiliations":[{"raw_affiliation_string":"LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I161929037","https://openalex.org/I4210119023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100421068","display_name":"Juan Li","orcid":"https://orcid.org/0000-0003-2415-8454"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juan Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044513568","display_name":"Marc Quincampoix","orcid":"https://orcid.org/0009-0004-4223-2720"},"institutions":[{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Quincampoix","raw_affiliation_strings":["LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)"],"affiliations":[{"raw_affiliation_string":"LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I161929037","https://openalex.org/I4210119023"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037725323","display_name":"J\u00e9r\u00f4me Renault","orcid":"https://orcid.org/0000-0003-2220-3143"},"institutions":[{"id":"https://openalex.org/I4210092408","display_name":"Toulouse School of Economics","ror":"https://ror.org/00ff5f522","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210092408"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Renault","raw_affiliation_strings":["TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)"],"affiliations":[{"raw_affiliation_string":"TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)","institution_ids":["https://openalex.org/I4210092408"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5013262276"],"corresponding_institution_ids":["https://openalex.org/I161929037","https://openalex.org/I2802204017","https://openalex.org/I4210119023"],"apc_list":null,"apc_paid":null,"fwci":0.7113,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7294451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"4","first_page":"1846","last_page":"1873"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9889000058174133,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9156192541122437},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5672784447669983},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.5313630104064941},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5261523127555847},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5185382962226868},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.48712706565856934},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.47418245673179626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43973278999328613},{"id":"https://openalex.org/keywords/equicontinuity","display_name":"Equicontinuity","score":0.42589133977890015},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42254838347435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3841199278831482},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3671863079071045}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9156192541122437},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5672784447669983},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.5313630104064941},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5261523127555847},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5185382962226868},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.48712706565856934},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.47418245673179626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43973278999328613},{"id":"https://openalex.org/C182539199","wikidata":"https://www.wikidata.org/wiki/Q249092","display_name":"Equicontinuity","level":2,"score":0.42589133977890015},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42254838347435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3841199278831482},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3671863079071045},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1169151","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169151","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:publications.ut-capitole.fr:41749","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401335","display_name":"Toulouse 1 Capitole Publications (Universit\u00e9 Toulouse I Capitole)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3131550300","host_organization_name":"Universit\u00e9 Toulouse-I-Capitole","host_organization_lineage":["https://openalex.org/I3131550300"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:publications.ut-capitole.fr:41749","is_oa":false,"landing_page_url":"https://www.idref.fr/08062488X>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401603","display_name":"Toulouse Capitole Publications (University Toulouse 1 Capitole)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3131550300","host_organization_name":"Universit\u00e9 Toulouse-I-Capitole","host_organization_lineage":["https://openalex.org/I3131550300"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:HAL:hal-02929156v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02929156","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2020, 58 (4), pp.1846-1873. &#x27E8;10.1137/18M1169151&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-04403012v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04403012","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0363-0129","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1724198840","display_name":null,"funder_award_id":"2018YFA0703900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4786065307","display_name":null,"funder_award_id":"11871037","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4923292763","display_name":null,"funder_award_id":"ANR-17-EUR-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8130988100","display_name":null,"funder_award_id":"ANR-16-CE40-0015-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324478","display_name":"Fondation Math\u00e9matique Jacques Hadamard","ror":"https://ror.org/0153me927"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W831507090","https://openalex.org/W838369491","https://openalex.org/W1481789702","https://openalex.org/W1691197524","https://openalex.org/W1985296147","https://openalex.org/W1992759804","https://openalex.org/W1995062337","https://openalex.org/W1995606924","https://openalex.org/W2000961292","https://openalex.org/W2006003117","https://openalex.org/W2011951499","https://openalex.org/W2012295020","https://openalex.org/W2039953262","https://openalex.org/W2067283326","https://openalex.org/W2068098627","https://openalex.org/W2076038142","https://openalex.org/W2076100084","https://openalex.org/W2096430401","https://openalex.org/W2149081875","https://openalex.org/W2185473163","https://openalex.org/W2557272457","https://openalex.org/W2963159681","https://openalex.org/W3098927100"],"related_works":["https://openalex.org/W2949333178","https://openalex.org/W3008145542","https://openalex.org/W2134654202","https://openalex.org/W2057711290","https://openalex.org/W2950551861","https://openalex.org/W3048177030","https://openalex.org/W4300889323","https://openalex.org/W4298162610","https://openalex.org/W2560165772","https://openalex.org/W2026069322"],"abstract_inverted_index":{"A":[0],"classical":[1],"problem":[2],"in":[3,21,66,200],"stochastic":[4,240],"ergodic":[5],"control":[6,156,241],"consists":[7],"of":[8,13,17,29,49,69,73,100,108,139,150,162,168,179,185,197,203,209,216,226],"studying":[9],"the":[10,14,34,42,54,63,67,105,109,112,128,148,151,155,177,183,194,210,214,217,223,234,244,256],"limit":[11,218],"behavior":[12],"optimal":[15],"value":[16,43,219],"a":[18,46,191],"discounted":[19],"integral":[20,31,51],"infinite":[22],"horizon":[23,55],"(the":[24],"so":[25],"called":[26],"Abel":[27,77,131,227],"mean":[28,48,230],"an":[30,50],"cost)":[32],"as":[33],"discount":[35],"factor":[36],"$\\lambda$":[37],"tends":[38,57],"to":[39,58,253],"zero":[40],"or":[41,79,133,228],"defined":[44,75],"with":[45],"Ces\u00e0ro":[47,134,229],"cost":[52],"when":[53,82,111,220],"$T$":[56],"$+":[59],"\\infty$.":[60],"We":[61,116,188],"investigate":[62],"possible":[64,123],"limits":[65,161],"norm":[68],"uniform":[70],"convergence":[71],"topology":[72],"values":[74,110],"through":[76],"means":[78,81,132],"Ce\u00e0ro":[80],"$":[83,87],"\\lambda":[84],"\\to":[85,90],"0^+":[86],"and":[88,154],"$T":[89],"+":[91],"\\infty":[92],"$,":[93],"respectively.":[94],"Here":[95],"we":[96],"give":[97,190],"two":[98],"types":[99],"new":[101],"representation":[102,140,169,204,211],"formulas":[103,212],"for":[104,130,236,238],"accumulation":[106,124],"points":[107],"averaging":[113],"parameter":[114],"converges.":[115],"show":[117],"that":[118],"there":[119],"is":[120,127,142,171,213,233],"only":[121],"one":[122,221],"point":[125],"which":[126,159,175,251],"same":[129],"means.":[135],"The":[136,165],"first":[137],"type":[138,167],"formula":[141,170],"based":[143,172],"on":[144,147,173,182],"probability":[145],"measures":[146,174,198],"product":[149],"state":[152,157],"space":[153,184],"space,":[158],"are":[160,176,249],"occupational":[163],"measures.":[164],"second":[166],"projection":[178],"invariant":[180],"measure":[181],"relaxed":[186],"controls.":[187],"also":[189],"result":[192],"comparing":[193],"both":[195,201],"sets":[196],"involved":[199],"classes":[202],"formulas.":[205],"An":[206],"important":[207],"consequence":[208],"existence":[215],"has":[222],"equicontinuity":[224],"property":[225],"values.":[231],"This":[232],"case,":[235],"example,":[237],"nonexpansive":[239],"systems.":[242],"In":[243],"end":[245],"some":[246],"insightful":[247],"examples":[248],"given":[250],"help":[252],"better":[254],"understand":[255],"results.":[257]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
