{"id":"https://openalex.org/W2000309010","doi":"https://doi.org/10.1137/140960086","title":"Multilevel Monte Carlo Approximation of Distribution Functions and Densities","display_name":"Multilevel Monte Carlo Approximation of Distribution Functions and Densities","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2000309010","doi":"https://doi.org/10.1137/140960086","mag":"2000309010"},"language":"en","primary_location":{"id":"doi:10.1137/140960086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140960086","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","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/A5056186758","display_name":"Michael B. Giles","orcid":"https://orcid.org/0000-0002-5445-3721"},"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":"Michael B. Giles","raw_affiliation_strings":["University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022858788","display_name":"Tigran Nagapetyan","orcid":"https://orcid.org/0000-0002-0379-1157"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tigran Nagapetyan","raw_affiliation_strings":["Weierstrass Institute"],"affiliations":[{"raw_affiliation_string":"Weierstrass Institute","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110337597","display_name":"Klaus Ritter","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Ritter","raw_affiliation_strings":["University of Kaiserslautern;"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern;","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056186758"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":12.8281,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.98697823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"267","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9975000023841858,"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":0.9975000023841858,"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":0.988099992275238,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9861000180244446,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.7120398283004761},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6385669708251953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5992343425750732},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.584751546382904},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5832175016403198},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5182766318321228},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.49991679191589355},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4499715566635132},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.44227468967437744},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.43743857741355896},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.42268407344818115},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3201278746128082},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24503013491630554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2402043342590332},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20353588461875916},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.16978609561920166},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16191759705543518}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7120398283004761},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6385669708251953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5992343425750732},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.584751546382904},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5832175016403198},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5182766318321228},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.49991679191589355},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4499715566635132},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.44227468967437744},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.43743857741355896},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.42268407344818115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3201278746128082},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24503013491630554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2402043342590332},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20353588461875916},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.16978609561920166},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16191759705543518},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/140960086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140960086","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.658.9513","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.658.9513","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dfg-spp1324.de/download/preprints/preprint157.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.713.1998","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.713.1998","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/juq_15.pdf","raw_type":"text"},{"id":"pmh:oai:fraunhofer.de:N-383298","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/N-383298.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer ITWM","raw_type":"Journal Article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:d0dd57ee-5116-4e79-ba71-f47c55075598","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:d0dd57ee-5116-4e79-ba71-f47c55075598","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/243540","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/243540","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/297168","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/297168","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1119182559","display_name":null,"funder_award_id":"EP/E031455/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7312442354","display_name":null,"funder_award_id":"EP/H05183X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":81,"referenced_works":["https://openalex.org/W70169678","https://openalex.org/W1504748373","https://openalex.org/W1511694993","https://openalex.org/W1535598240","https://openalex.org/W1548426124","https://openalex.org/W1770078204","https://openalex.org/W1964072990","https://openalex.org/W1967224735","https://openalex.org/W1968532092","https://openalex.org/W1969387119","https://openalex.org/W1969804920","https://openalex.org/W1970942811","https://openalex.org/W1972337987","https://openalex.org/W1975295794","https://openalex.org/W1976554733","https://openalex.org/W1976675231","https://openalex.org/W1979098872","https://openalex.org/W1982097817","https://openalex.org/W1983354332","https://openalex.org/W1988645907","https://openalex.org/W1995772505","https://openalex.org/W1999037361","https://openalex.org/W2002939700","https://openalex.org/W2004973016","https://openalex.org/W2006367766","https://openalex.org/W2014660679","https://openalex.org/W2017696609","https://openalex.org/W2020928358","https://openalex.org/W2023446392","https://openalex.org/W2024591553","https://openalex.org/W2026132654","https://openalex.org/W2031024722","https://openalex.org/W2032591190","https://openalex.org/W2032872151","https://openalex.org/W2032894334","https://openalex.org/W2035517047","https://openalex.org/W2039055345","https://openalex.org/W2044203216","https://openalex.org/W2048459485","https://openalex.org/W2052162576","https://openalex.org/W2062085624","https://openalex.org/W2066525883","https://openalex.org/W2066658881","https://openalex.org/W2069714153","https://openalex.org/W2070388948","https://openalex.org/W2074297971","https://openalex.org/W2077315519","https://openalex.org/W2077788007","https://openalex.org/W2080732943","https://openalex.org/W2082465502","https://openalex.org/W2083484777","https://openalex.org/W2094226191","https://openalex.org/W2096699795","https://openalex.org/W2098691865","https://openalex.org/W2116504170","https://openalex.org/W2117358914","https://openalex.org/W2122862651","https://openalex.org/W2140031057","https://openalex.org/W2140414732","https://openalex.org/W2148439964","https://openalex.org/W2154733290","https://openalex.org/W2156566935","https://openalex.org/W2162870748","https://openalex.org/W2163715525","https://openalex.org/W2164158544","https://openalex.org/W2223371834","https://openalex.org/W2364128533","https://openalex.org/W2463118743","https://openalex.org/W2586824433","https://openalex.org/W2607399731","https://openalex.org/W2951153688","https://openalex.org/W2951205186","https://openalex.org/W2964335503","https://openalex.org/W2997679055","https://openalex.org/W3098446318","https://openalex.org/W3098901429","https://openalex.org/W3099047247","https://openalex.org/W3103743465","https://openalex.org/W3105063129","https://openalex.org/W3106165169","https://openalex.org/W3124776929"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W1993992974","https://openalex.org/W1512294453","https://openalex.org/W2738234280","https://openalex.org/W2550734047","https://openalex.org/W2911841387","https://openalex.org/W2341571017","https://openalex.org/W4316143821"],"abstract_inverted_index":{"We":[0,35,49],"construct":[1],"and":[2,14,46,56,59],"analyze":[3],"multilevel":[4],"Monte":[5],"Carlo":[6],"methods":[7],"for":[8],"the":[9,23,44,51],"approximation":[10],"of":[11,16,64],"distribution":[12,25],"functions":[13],"densities":[15],"univariate":[17],"random":[18],"variables.":[19],"Since,":[20],"by":[21],"assumption,":[22],"target":[24],"is":[26],"not":[27],"known":[28],"explicitly,":[29],"approximations":[30],"have":[31],"to":[32,53,60],"be":[33],"used.":[34],"provide":[36],"a":[37],"general":[38],"analysis":[39],"under":[40],"suitable":[41],"assumptions":[42],"on":[43],"weak":[45],"strong":[47],"convergence.":[48],"apply":[50],"results":[52],"smooth":[54],"path-independent":[55],"path-dependent":[57],"functionals":[58],"stopped":[61],"exit":[62],"times":[63],"stochastic":[65],"differential":[66],"equations":[67],"(SDEs).":[68]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
