{"id":"https://openalex.org/W2952942833","doi":"https://doi.org/10.1137/15m1023014","title":"Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities","display_name":"Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2952942833","doi":"https://doi.org/10.1137/15m1023014","mag":"2952942833"},"language":"en","primary_location":{"id":"doi:10.1137/15m1023014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1023014","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.1501.04477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005237318","display_name":"Erhan Bayraktar","orcid":"https://orcid.org/0000-0002-1926-4570"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erhan Bayraktar","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS UNIVERSITY OF MICHIGAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS UNIVERSITY OF MICHIGAN","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037009650","display_name":"Andrea Cosso","orcid":"https://orcid.org/0000-0001-6020-0213"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Cosso","raw_affiliation_strings":["Dipartimento di Matematica - Politecnico di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica - Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055802354","display_name":"Huy\u00ean Pham","orcid":"https://orcid.org/0000-0002-1847-7750"},"institutions":[{"id":"https://openalex.org/I4210137396","display_name":"Centre de Recherche en \u00c9conomie et Statistique","ror":"https://ror.org/0449khs19","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I4210108488","https://openalex.org/I4210108488","https://openalex.org/I4210137396","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210150854","https://openalex.org/I84009706"]},{"id":"https://openalex.org/I4210128656","display_name":"Laboratoire de Biologie Physico-Chimique des Prot\u00e9ines Membranaires","ror":"https://ror.org/03nr8xh07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210096427","https://openalex.org/I4210128656"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Huy\u00ean Pham","raw_affiliation_strings":["Centre de Recherche en \u00c9conomie et Statistique","Laboratoire des Prot\u00e9ines et Syst\u00e8mes Membranaires"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Recherche en \u00c9conomie et Statistique","institution_ids":["https://openalex.org/I4210137396"]},{"raw_affiliation_string":"Laboratoire des Prot\u00e9ines et Syst\u00e8mes Membranaires","institution_ids":["https://openalex.org/I4210128656"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005237318"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29655712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"3","first_page":"1915","last_page":"1953"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.3109000027179718,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.3109000027179718,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.1526000052690506,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.10320000350475311,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.8146786689758301},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6501790285110474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.558167040348053},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5131915211677551},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49012455344200134},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4676980972290039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4430012106895447},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.40963679552078247},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33389681577682495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30117154121398926},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22668766975402832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2044951617717743},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13982459902763367},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10335859656333923},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05929994583129883}],"concepts":[{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.8146786689758301},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6501790285110474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.558167040348053},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5131915211677551},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49012455344200134},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4676980972290039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4430012106895447},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.40963679552078247},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33389681577682495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30117154121398926},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22668766975402832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2044951617717743},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13982459902763367},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10335859656333923},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05929994583129883}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1023014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1023014","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:HAL:hal-01104773v2","is_oa":false,"landing_page_url":"https://hal.science/hal-01104773","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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, 2017, 55 (3), pp.1915-1953. ⟨10.1137/15M1023014⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-03947551v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03947551","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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, 2017, 55 (3), pp.1915-1953. ⟨10.1137/15M1023014⟩","raw_type":"Journal articles"},{"id":"pmh:oai:cris.unibo.it:11585/610858","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/610858","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1501.04477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1501.04477","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.1501.04477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1501.04477","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6800000071525574,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1105273897","display_name":null,"funder_award_id":"DMS-1613170","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7380039393","display_name":"New Problems in Stochastic Control Motivated by Mathematical Finance","funder_award_id":"1613170","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W51876359","https://openalex.org/W1487586009","https://openalex.org/W1647881072","https://openalex.org/W1971594473","https://openalex.org/W1978646054","https://openalex.org/W1979055678","https://openalex.org/W1981444033","https://openalex.org/W1992759804","https://openalex.org/W1992992411","https://openalex.org/W2004745280","https://openalex.org/W2007374447","https://openalex.org/W2018676027","https://openalex.org/W2028836744","https://openalex.org/W2032316144","https://openalex.org/W2053068479","https://openalex.org/W2055222255","https://openalex.org/W2060878939","https://openalex.org/W2071447885","https://openalex.org/W2072321868","https://openalex.org/W2072444746","https://openalex.org/W2087985205","https://openalex.org/W2093303153","https://openalex.org/W2098244917","https://openalex.org/W2108101768","https://openalex.org/W2110939869","https://openalex.org/W2119993310","https://openalex.org/W2124430714","https://openalex.org/W2140171702","https://openalex.org/W2142784070","https://openalex.org/W2157509603","https://openalex.org/W2166451400","https://openalex.org/W2178442254","https://openalex.org/W2211926250","https://openalex.org/W2233780866","https://openalex.org/W2237183768","https://openalex.org/W2240853142","https://openalex.org/W2592216957","https://openalex.org/W2949413837","https://openalex.org/W2950127401","https://openalex.org/W2952855394","https://openalex.org/W2964304505","https://openalex.org/W3098963892","https://openalex.org/W3105343238","https://openalex.org/W3125380953","https://openalex.org/W3125933830","https://openalex.org/W4243590097"],"related_works":["https://openalex.org/W2053734433","https://openalex.org/W2094437620","https://openalex.org/W2106967042","https://openalex.org/W2016648763","https://openalex.org/W2018854980","https://openalex.org/W2115030441","https://openalex.org/W2067593096","https://openalex.org/W2353153612","https://openalex.org/W809330864","https://openalex.org/W1914388985"],"abstract_inverted_index":{"We":[0,42],"analyze":[1],"the":[2,46,58,64,68,73,102,120,123],"asymptotic":[3],"behavior":[4],"for":[5,119],"a":[6,79,82,93,114],"system":[7,66,84,124],"of":[8,81,85,125],"fully":[9],"nonlinear":[10,83],"parabolic":[11,65],"and":[12,31,96,111],"elliptic":[13,74],"quasi-variational":[14],"inequalities.":[15,88,127],"These":[16],"equations":[17],"are":[18],"related":[19],"to":[20,50,56,63,72,122],"robust":[21],"switching":[22],"control":[23],"problems":[24],"introduced":[25],"in":[26,112],"[E.":[27],"Bayraktar,":[28],"A.":[29],"Cosso,":[30],"H.":[32],"Pham,":[33],"SIAM":[34],"J.":[35],"Control":[36],"Optim.,":[37],"54":[38],"(2016),":[39],"pp.":[40],"2594--2628].":[41],"prove":[43],"that,":[44],"as":[45],"time":[47],"horizon":[48],"goes":[49,55],"infinity":[51],"(resp.,":[52,67],"discount":[53],"factor":[54],"zero),":[57],"long":[59],"run":[60],"average":[61],"solution":[62,71,80,121],"limiting":[69],"discounted":[70],"system)":[75],"is":[76],"characterized":[77],"by":[78],"ergodic":[86],"variational":[87,126],"Our":[89,105],"results":[90],"hold":[91],"under":[92],"dissipativity":[94],"condition":[95],"without":[97],"any":[98],"nondegeneracy":[99],"assumption":[100],"on":[101],"diffusion":[103],"term.":[104],"approach":[106],"uses":[107],"mainly":[108],"probabilistic":[109],"arguments":[110],"particular":[113],"dual":[115],"randomized":[116],"game":[117],"representation":[118]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2019-06-27T00:00:00"}