{"id":"https://openalex.org/W4403343528","doi":"https://doi.org/10.1007/s11222-024-10497-3","title":"Double-loop importance sampling for McKean\u2013Vlasov stochastic differential equation","display_name":"Double-loop importance sampling for McKean\u2013Vlasov stochastic differential equation","publication_year":2024,"publication_date":"2024-10-12","ids":{"openalex":"https://openalex.org/W4403343528","doi":"https://doi.org/10.1007/s11222-024-10497-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-024-10497-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-024-10497-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-024-10497-3.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/s11222-024-10497-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074019505","display_name":"Nadhir Ben Rached","orcid":"https://orcid.org/0000-0003-4471-4075"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nadhir Ben Rached","raw_affiliation_strings":["Department of Statistics, School of Mathematics, University of Leeds, Leeds, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, School of Mathematics, University of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","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/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Abdul-Lateef Haji-Ali","raw_affiliation_strings":["Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104142709","display_name":"Shyam Mohan Subbiah Pillai","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Shyam Mohan Subbiah Pillai","raw_affiliation_strings":["Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"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"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE","SA"],"is_corresponding":false,"raw_author_name":"Ra\u00fal Tempone","raw_affiliation_strings":["Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany","Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5104142709"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":2.8614,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.91473066,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"34","issue":"6","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":0.9965999722480774,"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":0.9965999722480774,"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/T11720","display_name":"Probability and Risk Models","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6949508190155029},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5605040192604065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5407465100288391},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5141163468360901},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43346500396728516},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.4304143190383911},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3356536328792572},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3115536868572235},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2824856638908386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17243963479995728}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6949508190155029},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5605040192604065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5407465100288391},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5141163468360901},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43346500396728516},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.4304143190383911},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3356536328792572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3115536868572235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2824856638908386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17243963479995728},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11222-024-10497-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-024-10497-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-024-10497-3.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"}],"best_oa_location":{"id":"doi:10.1007/s11222-024-10497-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-024-10497-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-024-10497-3.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":[{"id":"https://openalex.org/G5181818582","display_name":null,"funder_award_id":"URF/1/2584-01-01","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403343528.pdf","grobid_xml":"https://content.openalex.org/works/W4403343528.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W5385147","https://openalex.org/W69072573","https://openalex.org/W182704713","https://openalex.org/W613018134","https://openalex.org/W1507126399","https://openalex.org/W1990838746","https://openalex.org/W2005874252","https://openalex.org/W2006981621","https://openalex.org/W2027132443","https://openalex.org/W2036957539","https://openalex.org/W2048743591","https://openalex.org/W2064200597","https://openalex.org/W2065172718","https://openalex.org/W2065407206","https://openalex.org/W2111034649","https://openalex.org/W2153906005","https://openalex.org/W2168448159","https://openalex.org/W2175103811","https://openalex.org/W2276441017","https://openalex.org/W2276496321","https://openalex.org/W2337000559","https://openalex.org/W2544951676","https://openalex.org/W2546505240","https://openalex.org/W2586952071","https://openalex.org/W2595486899","https://openalex.org/W2771020255","https://openalex.org/W2913860142","https://openalex.org/W2939677525","https://openalex.org/W2952469530","https://openalex.org/W2962904725","https://openalex.org/W2963412531","https://openalex.org/W3105822863","https://openalex.org/W3105842177","https://openalex.org/W3125426943","https://openalex.org/W3126762542","https://openalex.org/W3137766651","https://openalex.org/W3167905296","https://openalex.org/W3180106877","https://openalex.org/W3207718143","https://openalex.org/W4205832274","https://openalex.org/W4212780424","https://openalex.org/W4231021340","https://openalex.org/W4319230502","https://openalex.org/W4361212142","https://openalex.org/W4362503231","https://openalex.org/W4389140755"],"related_works":["https://openalex.org/W24774503","https://openalex.org/W2014821076","https://openalex.org/W1990620319","https://openalex.org/W1965744717","https://openalex.org/W2111234595","https://openalex.org/W3216334292","https://openalex.org/W1883238101","https://openalex.org/W2481821631","https://openalex.org/W1536525683","https://openalex.org/W2482256034"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"investigates":[3],"Monte":[4],"Carlo":[5],"(MC)":[6],"methods":[7],"to":[8,18,97,125,219,245,258],"estimate":[9,247],"probabilities":[10],"of":[11,42,63,66,76,81,93,153,180,191,278],"rare":[12],"events":[13],"associated":[14],"with":[15,214,243,271],"the":[16,19,79,133,154,181,276,285],"solution":[17],"d":[20,45,145],"-dimensional":[21,46,115,146],"McKean\u2013Vlasov":[22],"stochastic":[23,33,47,85,98],"differential":[24,48,117],"equation":[25,119],"(MV-SDE).":[26],"MV-SDEs":[27],"are":[28,282],"usually":[29],"approximated":[30],"using":[31,84],"a":[32,40,55,72,103,144,150,163,173,185,215,221,260],"interacting":[34],"P":[35,43],"-particle":[36],"system,":[37],"which":[38,121],"is":[39,54,95,122],"set":[41],"coupled":[44],"equations":[49],"(SDEs).":[50],"Importance":[51],"sampling":[52],"(IS)":[53],"common":[56],"technique":[57],"for":[58,78,149],"reducing":[59,251],"high":[60],"relative":[61,223,252],"variance":[62,253],"MC":[64,168,273],"estimators":[65,274],"rare-event":[67,248],"probabilities.":[68],"We":[69,171],"first":[70],"derive":[71],"zero-variance":[73,151],"IS":[74,244],"change":[75,92],"measure":[77,94],"quantity":[80],"interest":[82],"by":[83],"optimal":[86,189],"control":[87,118,147],"theory.":[88],"However,":[89],"when":[90],"this":[91,129,159],"applied":[96],"particle":[99],"systems,":[100],"it":[101],"yields":[102],"$$P":[104],"\\times":[105],"d$$":[106],"<mml:math":[107,196,227,263],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[108,197,228,264],"<mml:mrow>":[109,198,203,206],"<mml:mi>P</mml:mi>":[110],"<mml:mo>\u00d7</mml:mo>":[111],"<mml:mi>d</mml:mi>":[112],"</mml:mrow>":[113,205,209,212],"</mml:math>":[114,213,233,269],"partial":[116],"(PDE),":[120],"computationally":[123,164],"expensive":[124],"solve.":[126],"To":[127],"address":[128],"issue,":[130],"we":[131,161,187,236],"use":[132],"decoupling":[134],"approach":[135],"introduced":[136],"in":[137,275],"(dos":[138],"Reis":[139],"et":[140],"al.":[141],"2023),":[142],"generating":[143],"PDE":[148],"estimator":[152],"decoupled":[155],"SDE.":[156],"Based":[157],"on":[158,284],"approach,":[160],"develop":[162],"efficient":[165],"double":[166],"loop":[167],"(DLMC)":[169],"estimator.":[170,183],"conduct":[172],"comprehensive":[174],"numerical":[175],"error":[176,224],"and":[177,254],"work":[178],"analysis":[179],"DLMC":[182,240],"As":[184],"result,":[186],"show":[188],"complexity":[190],"$$\\mathcal":[192],"{O}\\left(":[193],"\\textrm{TOL}_{\\textrm{r}}^{-4}\\right)":[194],"$$":[195],"<mml:mi>O</mml:mi>":[199],"<mml:mfenced>":[200],"<mml:msubsup>":[201],"<mml:mtext>TOL</mml:mtext>":[202,230,266],"<mml:mtext>r</mml:mtext>":[204,231,267],"<mml:mo>-</mml:mo>":[207],"<mml:mn>4</mml:mn>":[208],"</mml:msubsup>":[210],"</mml:mfenced>":[211],"significantly":[216],"reduced":[217],"constant":[218],"achieve":[220,259],"prescribed":[222],"tolerance":[225],"$$\\textrm{TOL}_{\\textrm{r}}$$":[226,262],"<mml:msub>":[229,265],"</mml:msub>":[232,268],".":[234],"Subsequently,":[235],"propose":[237],"an":[238],"adaptive":[239],"method":[241],"combined":[242],"numerically":[246],"probabilities,":[249],"substantially":[250],"computational":[255],"runtimes":[256],"required":[257],"given":[261],"compared":[270],"standard":[272],"absence":[277],"IS.":[279],"Numerical":[280],"experiments":[281],"performed":[283],"Kuramoto":[286],"model":[287],"from":[288],"statistical":[289],"physics.":[290]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2024-10-12T00:00:00"}