{"id":"https://openalex.org/W2465953938","doi":"https://doi.org/10.1137/15m1015583","title":"Weak Solutions of Mean-Field Stochastic Differential Equations and Application to Zero-Sum Stochastic Differential Games","display_name":"Weak Solutions of Mean-Field Stochastic Differential Equations and Application to Zero-Sum Stochastic Differential Games","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2465953938","doi":"https://doi.org/10.1137/15m1015583","mag":"2465953938"},"language":"en","primary_location":{"id":"doi:10.1137/15m1015583","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1015583","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/A5100421016","display_name":"Juan Li","orcid":"https://orcid.org/0000-0002-3300-0766"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Juan Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102933987","display_name":"Hui Min","orcid":"https://orcid.org/0000-0003-3491-9800"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hui Min","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100421016"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.666,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.97086191,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"54","issue":"3","first_page":"1826","last_page":"1858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9682000279426575,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9656999707221985,"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":0.871254026889801},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7271854877471924},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7039385437965393},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6627938747406006},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.5544485449790955},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5108153820037842},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.42225778102874756},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1303679347038269},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07687646150588989},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07407265901565552}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.871254026889801},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7271854877471924},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7039385437965393},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6627938747406006},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.5544485449790955},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5108153820037842},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.42225778102874756},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1303679347038269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07687646150588989},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07407265901565552}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1015583","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1015583","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.75,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1985296147","https://openalex.org/W2007734734","https://openalex.org/W2011961946","https://openalex.org/W2020652559","https://openalex.org/W2027729220","https://openalex.org/W2033603136","https://openalex.org/W2033677516","https://openalex.org/W2037222021","https://openalex.org/W2038686546","https://openalex.org/W2041869614","https://openalex.org/W2045352660","https://openalex.org/W2046047743","https://openalex.org/W2048743591","https://openalex.org/W2059900018","https://openalex.org/W2059922898","https://openalex.org/W2071986228","https://openalex.org/W2075099603","https://openalex.org/W2083051656","https://openalex.org/W2092569083","https://openalex.org/W2119062437","https://openalex.org/W2136519287","https://openalex.org/W2503537357","https://openalex.org/W2951714068","https://openalex.org/W3098633897"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2037140903","https://openalex.org/W2964120842","https://openalex.org/W4377938812","https://openalex.org/W2570224107","https://openalex.org/W4301104327","https://openalex.org/W4320924209","https://openalex.org/W2036330223","https://openalex.org/W2498369366","https://openalex.org/W4312782710"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,17,36,121,158,188],"devoted":[3],"to":[4,22,41,108,166,193],"the":[5,23,26,47,50,54,57,65,124,129,137,140,143,167,194],"study":[6,168],"of":[7,25,49,56,101,123,142,145,163,169],"stochastic":[8,172],"differential":[9,173],"equations":[10],"(SDEs)":[11],"whose":[12,185],"diffusion":[13],"coefficient":[14,33,187],"$\\sigma(s,X_{\\cdot\\wedge":[15],"s})$":[16],"Lipschitz":[18],"continuous":[19],"with":[20,39,71,106,153,183,191],"respect":[21,40,107,192],"path":[24],"solution":[27,58],"process":[28],"$X$,":[29],"while":[30],"its":[31],"drift":[32,186],"$b(s,X_{\\cdot\\wedge":[34,102],"s},Q_{X_s})$":[35,103],"only":[37,98,189],"measurable":[38,190],"$X$":[42],"and":[43,86,88,116,139,155],"depends":[44],"continuously":[45],"(in":[46],"sense":[48],"1-Wasserstein":[51],"metric)":[52],"on":[53,136],"law":[55,132],"process.":[59,196],"Embedded":[60],"in":[61,104,131,151,160],"a":[62,109,146],"mean-field":[63,72,125,180],"game,":[64],"weak":[66,110,147],"existence":[67,144],"for":[68,113,133],"such":[69],"SDEs":[70,182],"term":[73],"was":[74],"recently":[75],"studied":[76],"by":[77,176],"Lacker":[78,89,117],"[Stochastic":[79],"Process.":[80],"Appl.,":[81],"125":[82],"(2015),":[83,94],"pp.":[84,95],"2856--2894]":[85],"Carmona":[87,115,154],"[Ann.":[90],"Appl.":[91],"Probab.,":[92],"25":[93],"1189--1231]":[96],"under":[97],"sequential":[99],"continuity":[100],"$Q_{X}$":[105],"topology,":[111],"but":[112],"uniqueness,":[114],"supposed":[118],"that":[119],"$b$":[120,134],"independent":[122],"term.":[126],"We":[127],"prove":[128],"uniqueness":[130],"depending":[135],"mean-field,":[138],"proof":[141],"solution,":[148],"relatively":[149],"short":[150],"comparison":[152],"Lacker's":[156],"work,":[157],"extended":[159],"section":[161],"5":[162],"this":[164],"paper":[165],"2-person":[170],"zero-sum":[171],"games":[174],"described":[175],"doubly":[177],"controlled":[178],"coupled":[179],"forward-backward":[181],"dynamics":[184],"state":[195]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-01T08:55:55.761014","created_date":"2025-10-10T00:00:00"}
