{"id":"https://openalex.org/W24418085","doi":"https://doi.org/10.1137/15m1024664","title":"Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise","display_name":"Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W24418085","doi":"https://doi.org/10.1137/15m1024664","mag":"24418085"},"language":"en","primary_location":{"id":"doi:10.1137/15m1024664","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1024664","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5003071783","display_name":"David F. Anderson","orcid":"https://orcid.org/0000-0002-2344-614X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David F. Anderson","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058486589","display_name":"Desmond J. Higham","orcid":"https://orcid.org/0000-0002-6635-3461"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Desmond J. Higham","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107072461","display_name":"Yu Sun","orcid":"https://orcid.org/0000-0003-3525-2753"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu Sun","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003071783"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":3.2818,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91516567,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"54","issue":"2","first_page":"505","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9993000030517578,"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":0.9993000030517578,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9796000123023987,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7417899966239929},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.7258156538009644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7109527587890625},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.674494743347168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5367943048477173},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.46387848258018494},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4532807469367981},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.43746793270111084},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.42674732208251953},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.4221244752407074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35074079036712646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25295329093933105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17570745944976807},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15579986572265625},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07181450724601746}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7417899966239929},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7258156538009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7109527587890625},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.674494743347168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5367943048477173},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.46387848258018494},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4532807469367981},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.43746793270111084},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.42674732208251953},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.4221244752407074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35074079036712646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25295329093933105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17570745944976807},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15579986572265625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07181450724601746},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1024664","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1024664","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:55299","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/75132.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:pure.ed.ac.uk:publications/1277678e-1674-4346-a36f-c4ba68d3b6f7","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11820/1277678e-1674-4346-a36f-c4ba68d3b6f7","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W172803389","https://openalex.org/W897674100","https://openalex.org/W1190414567","https://openalex.org/W1275718198","https://openalex.org/W1485446321","https://openalex.org/W1509581155","https://openalex.org/W1511563235","https://openalex.org/W1575104486","https://openalex.org/W1587029759","https://openalex.org/W1620414136","https://openalex.org/W1903005089","https://openalex.org/W1981041832","https://openalex.org/W2013440660","https://openalex.org/W2021426723","https://openalex.org/W2024159878","https://openalex.org/W2025492874","https://openalex.org/W2043938372","https://openalex.org/W2046451925","https://openalex.org/W2050083387","https://openalex.org/W2050959157","https://openalex.org/W2053801198","https://openalex.org/W2073644805","https://openalex.org/W2078959038","https://openalex.org/W2120466844","https://openalex.org/W2122828856","https://openalex.org/W2124508608","https://openalex.org/W2136618953","https://openalex.org/W2137519698","https://openalex.org/W2149025384","https://openalex.org/W2155290264","https://openalex.org/W2157296221","https://openalex.org/W2163715525","https://openalex.org/W2185209740","https://openalex.org/W2962834951","https://openalex.org/W3095114851","https://openalex.org/W3099404592","https://openalex.org/W3101256565","https://openalex.org/W3101471540","https://openalex.org/W3104248402"],"related_works":["https://openalex.org/W946352265","https://openalex.org/W2189596786","https://openalex.org/W4382053489","https://openalex.org/W2089955609","https://openalex.org/W2039299714","https://openalex.org/W2466040413","https://openalex.org/W4383710307","https://openalex.org/W4307700932","https://openalex.org/W4388919052","https://openalex.org/W2119732617"],"abstract_inverted_index":{"We":[0,25],"consider":[1,26],"the":[2,19,39,57,62,65,76,87,94,102,113,132,151],"problem":[3],"of":[4,8,85,112,119],"numerically":[5],"estimating":[6],"expectations":[7],"solutions":[9],"to":[10,38,74,92,109,130,141,149],"stochastic":[11],"differential":[12],"equations":[13],"driven":[14],"by":[15],"Brownian":[16],"motions":[17],"in":[18,101,126],"commonly":[20],"occurring":[21],"small":[22,40],"noise":[23,41],"regime.":[24],"(i)":[27],"standard":[28,53],"Monte":[29,47],"Carlo":[30,48],"methods":[31],"combined":[32,50,68],"with":[33,51,69],"numerical":[34],"discretization":[35],"algorithms":[36],"tailored":[37],"setting,":[42],"and":[43],"(ii)":[44],"a":[45,52,82,117],"multilevel":[46,66,88],"method":[49,67,89],"Euler--Maruyama":[54,70],"implementation.":[55],"Under":[56],"assumptions":[58],"we":[59,106],"make":[60],"on":[61],"underlying":[63],"model,":[64],"is":[71,90,129],"often":[72],"found":[73,91],"be":[75],"most":[77],"efficient":[78],"option.":[79],"Moreover,":[80],"under":[81],"wide":[83],"range":[84],"scalings":[86],"give":[93],"same":[95],"asymptotic":[96,152],"complexity":[97],"that":[98],"would":[99],"arise":[100],"idealized":[103],"case":[104],"where":[105],"have":[107],"access":[108],"exact":[110],"samples":[111],"required":[114],"distribution":[115],"at":[116],"cost":[118],"$O(1)$":[120],"per":[121],"sample.":[122],"A":[123],"key":[124],"step":[125],"our":[127],"analysis":[128],"analyze":[131],"variance":[133],"between":[134],"two":[135],"coupled":[136],"paths":[137],"directly,":[138],"as":[139],"opposed":[140],"their":[142],"$L^2$":[143],"distance.":[144],"Careful":[145],"simulations":[146],"are":[147],"provided":[148],"illustrate":[150],"results.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}