{"id":"https://openalex.org/W7214041672","doi":"https://doi.org/10.48550/arxiv.2609.24849","title":"Quantitative finite-population approximation of heterogeneous linear--quadratic mean-field control with common noise","display_name":"Quantitative finite-population approximation of heterogeneous linear--quadratic mean-field control with common noise","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214041672","doi":"https://doi.org/10.48550/arxiv.2609.24849"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24849","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24849","pdf_url":"https://arxiv.org/pdf/2609.24849","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/2609.24849","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129509888","display_name":"Aqib Ahmed","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123185442","display_name":"Reykjav\u00edk University","ror":"https://ror.org/05d2kyx68","country_code":"IS","type":"education","lineage":["https://openalex.org/I123185442"]}],"countries":["IS"],"is_corresponding":true,"raw_author_name":"Ahmed, Aqib","raw_affiliation_strings":["Reykjavik University , Department of Engineering , aqib24"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Reykjavik University , Department of Engineering , aqib24","institution_ids":["https://openalex.org/I123185442"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5129509888"],"corresponding_institution_ids":["https://openalex.org/I123185442"],"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":0.9994999766349792,"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":0.9994999766349792,"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":0.0,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0,"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/mean-field-control","display_name":"mean-field control","score":0.8679999709129333},{"id":"https://openalex.org/keywords/common-noise","display_name":"common noise","score":0.8190000057220459},{"id":"https://openalex.org/keywords/random-parameters","display_name":"random coefficients","score":0.6790000200271606},{"id":"https://openalex.org/keywords/stochastic-riccati-equation","display_name":"stochastic Riccati equation","score":0.8009999990463257},{"id":"https://openalex.org/keywords/heterogeneous-agents","display_name":"heterogeneous agents","score":0.6399999856948853},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.640999972820282},{"id":"https://openalex.org/keywords/decentralized-control","display_name":"decentralized control","score":0.34599998593330383},{"id":"https://openalex.org/keywords/optimal-feedback-control","display_name":"optimal feedback control","score":0.4699999988079071},{"id":"https://openalex.org/keywords/interaction-kernel","display_name":"interaction kernel","score":0.6119999885559082},{"id":"https://openalex.org/keywords/linear-quadratic-control","display_name":"linear quadratic control","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522000074386597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49639999866485596},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4198000133037567},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3991999924182892},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.3686000108718872},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34450000524520874},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.32519999146461487},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.2937999963760376},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.288100004196167},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2515999972820282},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24849","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24849","pdf_url":"https://arxiv.org/pdf/2609.24849","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.2609.24849","doi":"https://doi.org/10.48550/arxiv.2609.24849","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24849","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24849","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24849","pdf_url":"https://arxiv.org/pdf/2609.24849","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":[],"funders":[{"id":"https://openalex.org/F4320309958","display_name":"Landsvirkjun","ror":"https://ror.org/03xn5qt57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214041672.pdf","grobid_xml":"https://content.openalex.org/works/W7214041672.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4415162385","https://openalex.org/W4416021366","https://openalex.org/W7106668013","https://openalex.org/W7128545265","https://openalex.org/W7136836796"],"related_works":["https://openalex.org/W4303613549","https://openalex.org/W4391074909","https://openalex.org/W2980365701","https://openalex.org/W3048620049","https://openalex.org/W2988205279","https://openalex.org/W2571136727","https://openalex.org/W2928295949","https://openalex.org/W2937255528","https://openalex.org/W4286306134","https://openalex.org/W6885034397"],"abstract_inverted_index":{"We":[0,49,106],"study":[1],"the":[2,20,39,55,60,70,94,97,102,111,120,133,147,151,175,181,188],"finite-population":[3,140],"approximation":[4,158],"of":[5,41,59,69,96,132],"a":[6,116,129,138],"heterogeneous":[7],"linear--quadratic":[8],"mean-field":[9],"control":[10],"problem":[11,24],"with":[12,54],"common":[13],"noise":[14],"and":[15,37,46,83,93,124,159],"random":[16],"coefficients.":[17],"Starting":[18],"from":[19],"centralized":[21],"social":[22,126],"planner":[23],"for":[25,174,183],"$N$":[26],"non-exchangeable":[27],"agents,":[28],"we":[29],"derive":[30],"its":[31,42,75],"exact":[32,90],"finite-dimensional":[33],"stochastic":[34],"Riccati":[35,57],"system":[36,53,58,177],"identify":[38],"scaling":[40],"diagonal,":[43],"off-diagonal,":[44],"affine,":[45],"scalar":[47],"components.":[48],"then":[50],"compare":[51],"this":[52],"Hilbert-space-valued":[56],"continuum":[61],"model.":[62],"Our":[63],"main":[64],"estimates":[65,109],"give":[66],"quantitative":[67],"convergence":[68],"complete":[71],"backward":[72,176],"system,":[73],"including":[74,170],"common-noise":[76,86],"martingale":[77],"integrands.":[78],"The":[79],"error":[80,152],"separates":[81],"coefficient":[82],"kernel":[84,100],"consistency,":[85],"approximation,":[87],"interface":[88],"effects,":[89],"diagonal":[91,104],"corrections,":[92],"mass":[95],"limiting":[98,134],"interaction":[99],"on":[101,164],"discrete":[103],"band.":[105],"propagate":[107],"these":[108,165],"to":[110,119],"feedback":[112,136],"gains":[113],"and,":[114],"by":[115],"cellwise":[117,130],"coupling,":[118],"optimal":[121,184],"states,":[122],"controls,":[123],"initial":[125],"values.":[127],"Finally,":[128],"projection":[131],"representative-agent":[135],"yields":[137],"decentralized":[139],"strategy":[141],"whose":[142],"optimality":[143],"gap":[144],"vanishes.":[145],"Under":[146],"stated":[148],"regularity":[149],"assumptions,":[150],"bounds":[153,163],"are":[154],"expressed":[155],"through":[156],"explicit":[157],"concentration":[160],"moduli.":[161],"Quantitative":[162],"moduli":[166],"yield":[167],"algebraic":[168],"rates,":[169],"an":[171],"$N^{-1/2}$":[172],"rate":[173],"in":[178],"finite-type":[179],"regimes;":[180],"rates":[182],"trajectories":[185],"additionally":[186],"reflect":[187],"available":[189],"conditional":[190],"moment":[191],"bounds.":[192]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}