{"id":"https://openalex.org/W7220377958","doi":"https://doi.org/10.48550/arxiv.2610.02467","title":"Fully Coupled Nonlinear Mean-Field FBS\u0394Es: Solvability and an LQ Buffer-Adjustment Illustration","display_name":"Fully Coupled Nonlinear Mean-Field FBS\u0394Es: Solvability and an LQ Buffer-Adjustment Illustration","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220377958","doi":"https://doi.org/10.48550/arxiv.2610.02467"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02467","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02467","pdf_url":"https://arxiv.org/pdf/2610.02467","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02467","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157429054","display_name":"Yingjie Zheng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou Normal University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng, Yingjie","raw_affiliation_strings":["Department of Mathematical Sciences , Huzhou Normal University , Huzhou 313000 , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Huzhou Normal University , Huzhou 313000 , Zhejiang , China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102014477","display_name":"Qingxin Meng","orcid":"https://orcid.org/0000-0003-4020-5679","observed_orcids":["https://orcid.org/0000-0003-4020-5679"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng, Qingxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5154568203","display_name":"Maoning Tang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou Normal University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tang, Maoning","raw_affiliation_strings":["Department of Mathematical Sciences , Huzhou Normal University , Huzhou 313000 , Zhejiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Huzhou Normal University , Huzhou 313000 , Zhejiang , China","institution_ids":["https://openalex.org/I3018263800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9984999895095825,"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":0.9984999895095825,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/open-loop-optimization","display_name":"open-loop optimization","score":0.6919999718666077},{"id":"https://openalex.org/keywords/scenario-tree","display_name":"scenario tree","score":0.5580000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.879800021648407},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6019999980926514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5789999961853027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5679000020027161},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5482000112533569},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5054000020027161},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37860000133514404},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3619000017642975},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3197999894618988},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C2777798563","wikidata":"https://www.wikidata.org/wiki/Q7603916","display_name":"State vector","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02467","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02467","pdf_url":"https://arxiv.org/pdf/2610.02467","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.02467","doi":"https://doi.org/10.48550/arxiv.2610.02467","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02467","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02467","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02467","pdf_url":"https://arxiv.org/pdf/2610.02467","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2818004746","display_name":"\u65e0\u9650\u7ef4\u5e73\u5747\u573a\u6b63\u5012\u5411\u968f\u673a\u53d1\u5c55\u7cfb\u7edf\u7406\u8bba\u53ca\u5176\u5e94\u7528","funder_award_id":"LZ22A010005","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G4485204376","display_name":null,"funder_award_id":"12271158","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220377958.pdf","grobid_xml":"https://content.openalex.org/works/W7220377958.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4406231631","https://openalex.org/W4408663037","https://openalex.org/W7160906576","https://openalex.org/W7212406423"],"related_works":["https://openalex.org/W4406231631","https://openalex.org/W7083476665","https://openalex.org/W4409743070","https://openalex.org/W4317802368","https://openalex.org/W2955382281","https://openalex.org/W4200409351","https://openalex.org/W2909204651","https://openalex.org/W4210609799","https://openalex.org/W4382363670","https://openalex.org/W4409853402"],"abstract_inverted_index":{"This":[0],"paper":[1],"establishes":[2],"sufficient":[3],"conditions":[4],"for":[5],"finite-horizon":[6],"solvability":[7],"of":[8,29],"fully":[9],"coupled":[10],"nonlinear":[11,111],"mean-field":[12,128],"forward--backward":[13],"stochastic":[14],"difference":[15],"equations":[16],"with":[17,37,113],"dependence":[18],"on":[19,41,98],"unconditional":[20],"first":[21],"moments.":[22],"The":[23,86],"forward":[24],"recursion":[25],"uses":[26],"conditional":[27],"projections":[28],"the":[30,38,62,99,106,120,133,139],"next":[31],"backward":[32],"state":[33,115],"and":[34,52,55,68,83,116],"its":[35,135],"product":[36],"innovation.":[39],"Building":[40],"existing":[42],"domination--monotonicity":[43],"methods,":[44],"we":[45],"formulate":[46],"deterministic":[47],"matrix":[48],"combinations":[49],"in":[50,61],"centered":[51],"mean":[53,117],"coordinates":[54],"prove":[56],"a":[57,74,80],"continuation":[58],"estimate":[59],"uniform":[60],"homotopy":[63],"parameter.":[64],"Global":[65],"Lipschitz":[66],"continuity":[67],"one":[69],"active":[70,87],"domination--coercivity":[71],"direction":[72],"yield":[73],"unique":[75,140],"square-integrable":[76],"adapted":[77],"solution,":[78],"an":[79,94],"priori":[81],"bound,":[82],"coefficient":[84],"stability.":[85],"parameter":[88],"can":[89],"be":[90],"normalized":[91],"without":[92],"imposing":[93],"additional":[95],"smallness":[96],"restriction":[97],"original":[100],"coefficients.":[101],"A":[102,110,126],"sign":[103],"transformation":[104],"handles":[105],"opposite":[107],"monotonicity":[108],"orientation.":[109],"example":[112],"saturating":[114],"interactions":[118],"verifies":[119],"assumptions,":[121],"including":[122],"degenerate":[123],"domination":[124],"directions.":[125],"scalar":[127],"LQ":[129],"buffer-adjustment":[130],"model":[131],"illustrates":[132],"theorem:":[134],"Hamiltonian":[136],"solution":[137],"characterizes":[138],"open-loop":[141],"optimizer.":[142],"An":[143],"exact":[144],"finite":[145],"scenario-tree":[146],"calculation":[147],"checks":[148],"this":[149],"characterization":[150],"against":[151],"direct":[152],"quadratic":[153],"optimization.":[154]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
