{"id":"https://openalex.org/W2964312068","doi":"https://doi.org/10.1137/18m118270x","title":"On the Error Rate of Conditional Quasi--Monte Carlo for Discontinuous Functions","display_name":"On the Error Rate of Conditional Quasi--Monte Carlo for Discontinuous Functions","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2964312068","doi":"https://doi.org/10.1137/18m118270x","mag":"2964312068"},"language":"en","primary_location":{"id":"doi:10.1137/18m118270x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m118270x","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/A5058665232","display_name":"Zhijian He","orcid":"https://orcid.org/0000-0002-0730-5953"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhijian He","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5058665232"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0419,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86045891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"57","issue":"2","first_page":"854","last_page":"874"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9764999747276306,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.7882599830627441},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6353636384010315},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6129668951034546},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.5529904961585999},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.5402085781097412},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5128281712532043},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5001814365386963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48613521456718445},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.48315972089767456},{"id":"https://openalex.org/keywords/conditional-variance","display_name":"Conditional variance","score":0.4557461738586426},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.4298233985900879},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.2067423164844513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19125184416770935},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16396406292915344},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.15671736001968384},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.13117167353630066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09191256761550903},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.07869783043861389}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7882599830627441},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6353636384010315},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6129668951034546},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.5529904961585999},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.5402085781097412},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5128281712532043},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5001814365386963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48613521456718445},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.48315972089767456},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.4557461738586426},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.4298233985900879},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2067423164844513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19125184416770935},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16396406292915344},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.15671736001968384},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.13117167353630066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09191256761550903},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.07869783043861389},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0},{"id":"https://openalex.org/C23922673","wikidata":"https://www.wikidata.org/wiki/Q180752","display_name":"Autoregressive conditional heteroskedasticity","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m118270x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m118270x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G353036145","display_name":null,"funder_award_id":"K5180420","funder_id":"https://openalex.org/F4320323059","funder_display_name":"South China University of Technology"},{"id":"https://openalex.org/G5989192156","display_name":"\u57fa\u4e8e\u62df\u8499\u7279\u5361\u7f57\u6a21\u62df\u7684VaR\u548cCVaR\u8ba1\u7b97\u95ee\u9898\u7814\u7a76","funder_award_id":"71601189","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323059","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W187931435","https://openalex.org/W1825668880","https://openalex.org/W1973738368","https://openalex.org/W1998105223","https://openalex.org/W2016770622","https://openalex.org/W2035206081","https://openalex.org/W2065021724","https://openalex.org/W2099220105","https://openalex.org/W2100179204","https://openalex.org/W2113753459","https://openalex.org/W2124189866","https://openalex.org/W2132851968","https://openalex.org/W2603486066","https://openalex.org/W2613329859","https://openalex.org/W2963818518","https://openalex.org/W4248381180"],"related_works":["https://openalex.org/W4238858747","https://openalex.org/W4213450758","https://openalex.org/W2351008179","https://openalex.org/W2592623155","https://openalex.org/W2137276647","https://openalex.org/W2592465853","https://openalex.org/W4213371211","https://openalex.org/W2054666095","https://openalex.org/W2808512302","https://openalex.org/W2063889005"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,27,46,115,121,125],"rate":[4,104],"of":[5,16,29,59,91,114,117,120,127],"convergence":[6],"for":[7,70,93],"conditional":[8,17,41,80],"quasi--Monte":[9],"Carlo":[10],"(QMC),":[11],"which":[12,31],"is":[13],"a":[14,88,98],"counterpart":[15],"Monte":[18],"Carlo.":[19],"We":[20],"focus":[21],"on":[22,26],"discontinuous":[23,122],"integrands":[24],"defined":[25],"whole":[28],"$\\mathbb{R}^d$,":[30],"can":[32,56],"be":[33],"unbounded.":[34],"Under":[35],"suitable":[36],"conditions,":[37],"we":[38,100],"show":[39],"that":[40,83,102],"QMC":[42,82,109],"not":[43],"only":[44],"has":[45],"smoothing":[47],"effect":[48],"(up":[49],"to":[50,66,107],"infinitely":[51],"times":[52],"differentiable)":[53],"but":[54],"also":[55,105],"bring":[57],"orders":[58],"magnitude":[60],"reduction":[61],"in":[62,74],"integration":[63,110],"error":[64,90],"compared":[65],"plain":[67],"QMC.":[68],"Particularly,":[69],"some":[71],"typical":[72],"problems":[73],"options":[75],"pricing":[76],"and":[77],"Greeks":[78],"estimation,":[79],"randomized":[81,108],"uses":[84],"$n$":[85],"samples":[86],"yields":[87],"mean":[89],"$O(n^{-1+\\epsilon})$":[92],"arbitrarily":[94],"small":[95],"$\\epsilon>0$.":[96],"As":[97],"byproduct,":[99],"find":[101],"this":[103],"applies":[106],"with":[111],"all":[112],"terms":[113],"analysis":[116],"variance":[118],"decomposition":[119],"integrand,":[123],"except":[124],"one":[126],"highest":[128],"order.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
