{"id":"https://openalex.org/W2091977478","doi":"https://doi.org/10.1515/mcma-2013-0014","title":"Implementation and analysis of an adaptive multilevel Monte Carlo algorithm","display_name":"Implementation and analysis of an adaptive multilevel Monte Carlo algorithm","publication_year":2013,"publication_date":"2013-11-13","ids":{"openalex":"https://openalex.org/W2091977478","doi":"https://doi.org/10.1515/mcma-2013-0014","mag":"2091977478"},"language":"en","primary_location":{"id":"doi:10.1515/mcma-2013-0014","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2013-0014","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"mcma","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-94108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064285892","display_name":"H\u00e5kon Hoel","orcid":"https://orcid.org/0000-0003-0723-6641"},"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":"H\u00e5kon Hoel","raw_affiliation_strings":["Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia","King Abdullah University of Science & Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"King Abdullah University of Science & Technology","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039534540","display_name":"Erik von Schwerin","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"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":["CH","SA"],"is_corresponding":false,"raw_author_name":"Erik von Schwerin","raw_affiliation_strings":["CSQI-MATHICSE, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland","King Abdullah University of Science & Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CSQI-MATHICSE, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"King Abdullah University of Science & Technology","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004805552","display_name":"Anders Szepessy","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anders Szepessy","raw_affiliation_strings":["Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"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/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SA","SE"],"is_corresponding":false,"raw_author_name":"Ra\u00fal Tempone","raw_affiliation_strings":["Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia","Royal Inst. of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"Royal Inst. of Technology","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7555,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.94969271,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"1","first_page":"1","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9950000047683716,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.5146516561508179},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5014679431915283},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.447787344455719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41240790486335754},{"id":"https://openalex.org/keywords/analytical-chemistry","display_name":"Analytical Chemistry (journal)","score":0.3596469759941101},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18389761447906494},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.12357503175735474}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5146516561508179},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5014679431915283},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.447787344455719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41240790486335754},{"id":"https://openalex.org/C113196181","wikidata":"https://www.wikidata.org/wiki/Q485223","display_name":"Analytical Chemistry (journal)","level":2,"score":0.3596469759941101},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18389761447906494},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.12357503175735474},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1515/mcma-2013-0014","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2013-0014","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"mcma","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.702.3778","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.702.3778","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/gilesm/files/Adaptive_Multi_Level_SDE.pdf","raw_type":"text"},{"id":"pmh:oai:DiVA.org:kth-94108","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-94108","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"},{"id":"pmh:oai:doc.rero.ch:296943","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400148","display_name":"reroDoc Digital Library","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:infoscience.epfl.ch:269487","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/269487","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/563323","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/563323","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:kth-94108","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-94108","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"},"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W105300439","https://openalex.org/W113227339","https://openalex.org/W198005673","https://openalex.org/W306712725","https://openalex.org/W568080693","https://openalex.org/W1561215347","https://openalex.org/W1575104486","https://openalex.org/W1577527822","https://openalex.org/W1580561995","https://openalex.org/W1602773783","https://openalex.org/W2000830638","https://openalex.org/W2004973016","https://openalex.org/W2010897718","https://openalex.org/W2019795760","https://openalex.org/W2021707151","https://openalex.org/W2023446392","https://openalex.org/W2050871708","https://openalex.org/W2055494344","https://openalex.org/W2056380017","https://openalex.org/W2063939409","https://openalex.org/W2066221740","https://openalex.org/W2096503624","https://openalex.org/W2100702226","https://openalex.org/W2103628129","https://openalex.org/W2117358914","https://openalex.org/W2124633501","https://openalex.org/W2137519698","https://openalex.org/W2139139723","https://openalex.org/W2163715525","https://openalex.org/W2163891345","https://openalex.org/W2169071224","https://openalex.org/W2576544140","https://openalex.org/W2794914128","https://openalex.org/W2799137445","https://openalex.org/W2989666100","https://openalex.org/W3105063129","https://openalex.org/W3142877496"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"present":[2],"an":[3,31,167],"adaptive":[4,199,233,362],"multilevel":[5],"Monte":[6,56],"Carlo":[7,57],"(MLMC)":[8],"method":[9,33,58,169,279],"for":[10,127,319,360],"weak":[11],"approximations":[12],"of":[13,38,132,173,188,220,249,274],"solutions":[14],"to":[15,45,82,366],"It\u00f4":[16],"stochastic":[17],"differential":[18],"equations":[19],"(SDE).":[20],"The":[21],"work":[22,155,196],"[Oper.":[23],"Res.":[24],"56":[25],"(2008),":[26],"607\u2013617]":[27],"proposed":[28],"and":[29,42,214,239,266],"analyzed":[30],"MLMC":[32,168,193,200,234],"based":[34],"on":[35],"a":[36,52,128,171,186,275],"hierarchy":[37,172],"uniform":[39,190,276],"time":[40,177,191],"discretizations":[41],"control":[43,248],"variates":[44],"reduce":[46],"the":[47,154,189,198,221,242,250,255,272,308,311,316,321,361],"computational":[48,317],"effort":[49],"required":[50],"by":[51],"single":[53,277,363],"level":[54,278,364],"Euler\u2013Maruyama":[55],"from":[59,337],"<m:math":[60,83,133,281,323,338,368],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[61,84,134,282,324,339,369],"<m:mrow>":[62,66,71,85,89,94,102,105,110,135,139,283,287,292,325,340,344,349,370,374,379,387],"<m:mi>\ud835\udcaa</m:mi>":[63,86,136,284,326,341,371],"<m:mo>(</m:mo>":[64,87,103,137,285,327,342,372],"<m:msup>":[65,88,101,104,138,286,343,373,386],"<m:mi>":[67,90,106,140,288,328,345,375],"TOL":[68,91,107,141,289,329,346,376],"</m:mi>":[69,92,108,142,290,330,347,377],"</m:mrow>":[70,74,77,93,97,109,113,116,120,143,147,291,295,298,332,348,352,355,378,382],"<m:mo>-</m:mo>":[72,95,111,293,350,380],"<m:mn>3</m:mn>":[73,351],"</m:msup>":[75,98,114,118,145,296,353,383],"<m:mo>)</m:mo>":[76,115,119,146,297,331,354],"</m:math>":[78,121,148,299,333,356],"${{{\\mathcal":[79,122,149,300,334,357],"{O}}({\\mathrm":[80,123,150,301,335,358],"{TOL}}^{-3})}}$":[81,359],"<m:mn>2</m:mn>":[96,117,144,381],"<m:mo":[99,384],"form=\"prefix\">log</m:mo>":[100,385],"<m:mn>1</m:mn>":[112],"{TOL}}^{-2}\\log":[124],"({\\mathrm":[125],"{TOL}}^{-1})^{2})}}$":[126],"mean":[129],"square":[130],"error":[131],"{TOL}}^2)}}$":[151],".":[152,303],"Later,":[153],"[Lect.":[156,204],"Notes":[157,205],"Comput.":[158,206],"Sci.":[159,207],"Eng.":[160,208],"82,":[161,209],"Springer-Verlag,":[162,210],"Berlin":[163,211],"(2012),":[164,212],"217\u2013234]":[165,213],"presented":[166,202],"using":[170],"adaptively":[174],"refined,":[175],"non-uniform":[176],"discretizations,":[178],"and,":[179],"as":[180],"such,":[181],"it":[182,215],"may":[183],"be":[184],"considered":[185],"generalization":[187],"discretization":[192],"method.":[194],"This":[195],"improves":[197],"algorithms":[201,235],"in":[203,254,315],"also":[216],"provides":[217],"mathematical":[218],"analysis":[219],"improved":[222,247],"algorithms.":[223],"In":[224],"particular,":[225],"we":[226],"show":[227],"that":[228],"under":[229],"some":[230],"assumptions":[231],"our":[232],"are":[236],"asymptotically":[237],"accurate":[238],"essentially":[240,367],"have":[241],"correct":[243],"complexity":[244,251,273],"but":[245],"with":[246,263,268],"constant":[252],"factor":[253],"asymptotic":[256],"analysis.":[257],"Numerical":[258],"tests":[259],"include":[260],"one":[261,267],"case":[262],"singular":[264],"drift":[265],"stopped":[269],"diffusion,":[270],"where":[271],"is":[280],"<m:mn>4</m:mn>":[294],"{TOL}}^{-4})}}$":[302],"For":[304],"both":[305],"these":[306],"cases":[307],"results":[309],"confirm":[310],"theory,":[312],"exhibiting":[313],"savings":[314],"cost":[318],"achieving":[320],"accuracy":[322],"{TOL}})}}$":[336],"algorithm":[365]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}