{"id":"https://openalex.org/W1971040045","doi":"https://doi.org/10.1109/tac.2013.2264550","title":"A Stochastic Maximum Principle for Delayed Mean-Field Stochastic Differential Equations and Its Applications","display_name":"A Stochastic Maximum Principle for Delayed Mean-Field Stochastic Differential Equations and Its Applications","publication_year":2013,"publication_date":"2013-05-21","ids":{"openalex":"https://openalex.org/W1971040045","doi":"https://doi.org/10.1109/tac.2013.2264550","mag":"1971040045"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2264550","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2264550","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5033127832","display_name":"Heng Du","orcid":"https://orcid.org/0000-0002-3489-4562"},"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":"Heng Du","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, China","Sch. of Math. & Stat., Shandong Univ., Weihai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"Sch. of Math. & Stat., Shandong Univ., Weihai, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075552347","display_name":"Jianhui Huang","orcid":"https://orcid.org/0000-0003-3315-6549"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jianhui Huang","raw_affiliation_strings":["The Hong Kong Polytechnic University","Hong Kong Polytech. Univ., Kowloon, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Hong Kong Polytech. Univ., Kowloon, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011683236","display_name":"Yongli Qin","orcid":"https://orcid.org/0000-0001-7124-1299"},"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":"Yongli Qin","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, China","Sch. of Math. & Stat., Shandong Univ., Weihai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"Sch. of Math. & Stat., Shandong Univ., Weihai, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8469,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.7878044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"58","issue":"12","first_page":"3212","last_page":"3217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991999864578247,"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":0.9991999864578247,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.733634352684021},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6947751045227051},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6661753058433533},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.6569942831993103},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.6018673181533813},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5788946151733398},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5446199774742126},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.49258142709732056},{"id":"https://openalex.org/keywords/stochastic-calculus","display_name":"Stochastic calculus","score":0.4483250677585602},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42742544412612915},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.3703870475292206},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3570979833602905},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3555270731449127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3315514028072357},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16305187344551086}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.733634352684021},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6947751045227051},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6661753058433533},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.6569942831993103},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.6018673181533813},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5788946151733398},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5446199774742126},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.49258142709732056},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.4483250677585602},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42742544412612915},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.3703870475292206},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3570979833602905},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3555270731449127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3315514028072357},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16305187344551086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2013.2264550","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2264550","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/12205","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/12205","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.44999998807907104,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1505057802","https://openalex.org/W1567092208","https://openalex.org/W1969717343","https://openalex.org/W1983321045","https://openalex.org/W1983997656","https://openalex.org/W1987280177","https://openalex.org/W2011000015","https://openalex.org/W2022384100","https://openalex.org/W2034377457","https://openalex.org/W2037152246","https://openalex.org/W2041212965","https://openalex.org/W2046241416","https://openalex.org/W2070249529","https://openalex.org/W2081207514","https://openalex.org/W2082657448","https://openalex.org/W2099365847","https://openalex.org/W2109948101","https://openalex.org/W2117783125","https://openalex.org/W2131355869","https://openalex.org/W2155099874","https://openalex.org/W2952444919","https://openalex.org/W2963997268","https://openalex.org/W3099900433","https://openalex.org/W3106272087","https://openalex.org/W4256232807"],"related_works":["https://openalex.org/W2951493195","https://openalex.org/W4296279024","https://openalex.org/W2081720351","https://openalex.org/W2884436972","https://openalex.org/W2076700910","https://openalex.org/W1972668253","https://openalex.org/W2110776584","https://openalex.org/W2022384100","https://openalex.org/W1971040045","https://openalex.org/W2293485771"],"abstract_inverted_index":{"In":[0,84,103],"this":[1,32],"technical":[2],"note,":[3],"we":[4,93],"discuss":[5],"the":[6,41,50,59,67,87,95,105,109,126],"stochastic":[7,13,63,69],"optimal":[8,70,133,140,163],"control":[9,71,134,141,164],"problems":[10,135],"of":[11,44,52,79,108],"mean-field":[12,56,68,128],"differential":[14],"delayed":[15,131],"equations":[16],"(MFSDDEs)":[17],"which":[18],"arise":[19],"naturally":[20],"from":[21],"various":[22],"backgrounds":[23],"including":[24],"economics,":[25],"finance,":[26],"engineering":[27],"and":[28,55,81,90,144,160],"physics,":[29],"etc.":[30],"To":[31],"end,":[33],"some":[34,115],"new":[35],"estimates":[36],"are":[37,136],"used":[38],"to":[39,49],"handle":[40],"complex":[42],"structure":[43],"our":[45,123],"controlled":[46],"system":[47],"due":[48],"presence":[51],"both":[53],"delay":[54,73],"characters.":[57],"As":[58,153],"main":[60],"result,":[61],"a":[62],"maximum":[64,124],"principle":[65],"for":[66,98],"with":[72],"(MFSOCD)":[74],"is":[75,111,142,147,157,165],"derived":[76,143],"in":[77],"terms":[78],"necessary":[80,96],"sufficient":[82,106],"conditions.":[83],"particular,":[85],"applying":[86],"convex":[88,116],"variation":[89],"duality":[91],"relation,":[92],"obtain":[94],"condition":[97,107,117],"optimality":[99,110],"(see":[100,118],"Theorem":[101,119,151],"1).":[102],"addition,":[104],"also":[112,137,148,158],"obtained":[113],"under":[114],"2).":[120],"Based":[121],"on":[122],"principle,":[125],"related":[127],"linear":[129],"quadratic":[130],"(MFLQD)":[132],"investigated.":[138],"The":[139],"its":[145,161],"existence":[146],"verified":[149],"(refer":[150],"3).":[152],"illustration,":[154],"an":[155],"example":[156],"proposed":[159],"explicit":[162],"derived.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
