{"id":"https://openalex.org/W2544951676","doi":"https://doi.org/10.1007/s11222-017-9771-5","title":"Multilevel and Multi-index Monte Carlo methods for the McKean\u2013Vlasov equation","display_name":"Multilevel and Multi-index Monte Carlo methods for the McKean\u2013Vlasov equation","publication_year":2017,"publication_date":"2017-09-12","ids":{"openalex":"https://openalex.org/W2544951676","doi":"https://doi.org/10.1007/s11222-017-9771-5","mag":"2544951676"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-017-9771-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-017-9771-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-017-9771-5.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-017-9771-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013203959","display_name":"Abdul-Lateef Haji-Ali","orcid":"https://orcid.org/0000-0002-6243-0335"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Abdul-Lateef Haji-Ali","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0002-6243-0335","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004939553","display_name":"Ra\u00fal Tempone","orcid":"https://orcid.org/0000-0003-1967-4446"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ra\u00fal Tempone","raw_affiliation_strings":["Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013203959"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":5.4967,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.95563011,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"923","last_page":"935"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9976999759674072,"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":0.9976999759674072,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9861000180244446,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9775000214576721,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.7622004747390747},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6613826751708984},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6496691107749939},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6056168079376221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6049387454986572},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4641593098640442},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.45575135946273804},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40390917658805847},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21487078070640564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20828017592430115},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08015599846839905}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7622004747390747},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6613826751708984},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6496691107749939},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6056168079376221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6049387454986572},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4641593098640442},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45575135946273804},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40390917658805847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21487078070640564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20828017592430115},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08015599846839905}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11222-017-9771-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-017-9771-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-017-9771-5.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/625499","is_oa":true,"landing_page_url":"http://hdl.handle.net/10754/625499","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s11222-017-9771-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-017-9771-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-017-9771-5.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2544951676.pdf","grobid_xml":"https://content.openalex.org/works/W2544951676.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W182704713","https://openalex.org/W589850804","https://openalex.org/W1575104486","https://openalex.org/W1595193945","https://openalex.org/W1835030294","https://openalex.org/W1990838746","https://openalex.org/W2010901168","https://openalex.org/W2014945091","https://openalex.org/W2021800242","https://openalex.org/W2024771618","https://openalex.org/W2039393861","https://openalex.org/W2048743591","https://openalex.org/W2064559544","https://openalex.org/W2077852080","https://openalex.org/W2083206954","https://openalex.org/W2106605796","https://openalex.org/W2117358914","https://openalex.org/W2119062437","https://openalex.org/W2135459060","https://openalex.org/W2163715525","https://openalex.org/W2167052694","https://openalex.org/W2168448159","https://openalex.org/W2216407598","https://openalex.org/W2254624766","https://openalex.org/W2276441017","https://openalex.org/W2906926620","https://openalex.org/W2963159856","https://openalex.org/W2964170546","https://openalex.org/W3103019089","https://openalex.org/W3106115551","https://openalex.org/W4231021340"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W2005266888"],"abstract_inverted_index":{"We":[0,136],"address":[1],"the":[2,19,23,35,39,67,73,87,100,103,111,128,132,143,156,169],"approximation":[3],"of":[4,10,25,38,53,69,75,86,107,121,160,175],"functionals":[5],"depending":[6],"on":[7,78,168],"a":[8,56,139,173],"system":[9,174],"particles,":[11],"described":[12],"by":[13],"stochastic":[14],"differential":[15],"equations":[16],"(SDEs),":[17],"in":[18,99,113,155],"mean-field":[20],"limit":[21],"when":[22,126],"number":[24,68,74],"particles":[26,54],"approaches":[27],"infinity.":[28],"This":[29],"problem":[30],"is":[31,125],"equivalent":[32],"to":[33,109],"estimating":[34],"weak":[36],"solution":[37],"limiting":[40],"McKean\u2013Vlasov":[41],"SDE.":[42],"To":[43],"that":[44,141],"end,":[45],"our":[46],"approach":[47],"uses":[48,142],"systems":[49],"with":[50,117],"finite":[51],"numbers":[52],"and":[55,72,90,96,131,149],"time-stepping":[57,134],"scheme.":[58,135],"In":[59],"this":[60],"case,":[61,102],"there":[62],"are":[63,165],"two":[64,80],"discretization":[65],"parameters:":[66],"time":[70],"steps":[71],"particles.":[76],"Based":[77],"these":[79],"parameters,":[81],"we":[82],"consider":[83,138],"different":[84],"variants":[85],"Monte":[88,92,146],"Carlo":[89,93,147],"Multilevel":[91],"(MLMC)":[94],"methods":[95],"show":[97,150],"that,":[98],"best":[101],"optimal":[104],"work":[105,153],"complexity":[106,154],"MLMC,":[108],"estimate":[110],"functional":[112],"one":[114],"typical":[115,158],"setting":[116,159],"an":[118,151],"error":[119],"tolerance":[120],"$$\\mathrm":[122],"{TOL}$$":[123],",":[124],"using":[127],"partitioning":[129],"estimator":[130],"Milstein":[133],"also":[137],"method":[140,148],"recent":[144],"Multi-index":[145],"improved":[152],"same":[157],".":[161],"Our":[162],"numerical":[163],"experiments":[164],"carried":[166],"out":[167],"so-called":[170],"Kuramoto":[171],"model,":[172],"coupled":[176],"oscillators.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
