{"id":"https://openalex.org/W3193891506","doi":"https://doi.org/10.1515/jnma-2021-0111","title":"Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations","display_name":"Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations","publication_year":2022,"publication_date":"2022-07-12","ids":{"openalex":"https://openalex.org/W3193891506","doi":"https://doi.org/10.1515/jnma-2021-0111","mag":"3193891506"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2021-0111","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0111","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical Mathematics","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/A5030623220","display_name":"Martin Hutzenthaler","orcid":"https://orcid.org/0000-0003-0738-8717"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Hutzenthaler","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen , Duisburg-Essen Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen , Duisburg-Essen Germany","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074382323","display_name":"Arnulf Jentzen","orcid":"https://orcid.org/0000-0002-9840-3339"},"institutions":[{"id":"https://openalex.org/I63274643","display_name":"FH M\u00fcnster","ror":"https://ror.org/00pv45a02","country_code":"DE","type":"education","lineage":["https://openalex.org/I63274643"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]},{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]},{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Arnulf Jentzen","raw_affiliation_strings":["Applied Mathematics M\u00fcnster, Faculty of Mathematics and Computer Science, University of M\u00fcnster , M\u00fcnster Germany","School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong , Shenzhen , China"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics M\u00fcnster, Faculty of Mathematics and Computer Science, University of M\u00fcnster , M\u00fcnster Germany","institution_ids":["https://openalex.org/I63274643","https://openalex.org/I22465464"]},{"raw_affiliation_string":"School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong , Shenzhen , China","institution_ids":["https://openalex.org/I4210116924","https://openalex.org/I4210099586"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036131671","display_name":"Thomas Kruse","orcid":"https://orcid.org/0000-0003-2388-3929"},"institutions":[{"id":"https://openalex.org/I4210148049","display_name":"Giessen School of Theology","ror":"https://ror.org/03kzgcv48","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210148049"]},{"id":"https://openalex.org/I200763008","display_name":"University of Giessen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Kruse","raw_affiliation_strings":["Institute of Mathematics, University of Gie\u00dfen , Gie\u00dfen Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Gie\u00dfen , Gie\u00dfen Germany","institution_ids":["https://openalex.org/I4210148049","https://openalex.org/I200763008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100665212","display_name":"Tuan Anh Nguyen","orcid":"https://orcid.org/0000-0003-0247-4333"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tuan Anh Nguyen","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen , Duisburg-Essen Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen , Duisburg-Essen Germany","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030623220"],"corresponding_institution_ids":["https://openalex.org/I62318514"],"apc_list":null,"apc_paid":null,"fwci":1.0158,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75588035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"0","issue":"0","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":0.9986000061035156,"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":0.9986000061035156,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.983299970626831,"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":0.9819999933242798,"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.67936110496521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6793540716171265},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6174393892288208},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5988362431526184},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.583723247051239},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5353729128837585},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46461379528045654},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32522162795066833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30428773164749146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.272320032119751},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12259680032730103},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09158000349998474},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.060063302516937256}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.67936110496521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6793540716171265},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6174393892288208},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5988362431526184},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.583723247051239},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5353729128837585},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46461379528045654},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32522162795066833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30428773164749146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.272320032119751},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12259680032730103},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09158000349998474},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.060063302516937256}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2021-0111","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0111","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":141,"referenced_works":["https://openalex.org/W33909759","https://openalex.org/W43426828","https://openalex.org/W84156084","https://openalex.org/W89754605","https://openalex.org/W94839203","https://openalex.org/W204256407","https://openalex.org/W204489328","https://openalex.org/W227905838","https://openalex.org/W579287291","https://openalex.org/W581123446","https://openalex.org/W592962635","https://openalex.org/W659339155","https://openalex.org/W1507126399","https://openalex.org/W1520669850","https://openalex.org/W1525883337","https://openalex.org/W1576861397","https://openalex.org/W1593490009","https://openalex.org/W1606518485","https://openalex.org/W1740091825","https://openalex.org/W1820164671","https://openalex.org/W1835030294","https://openalex.org/W1948872067","https://openalex.org/W1972194505","https://openalex.org/W1974555191","https://openalex.org/W1980091117","https://openalex.org/W1981151146","https://openalex.org/W1982008399","https://openalex.org/W1994791309","https://openalex.org/W1999483367","https://openalex.org/W2004794023","https://openalex.org/W2004973016","https://openalex.org/W2005018490","https://openalex.org/W2007567546","https://openalex.org/W2012285732","https://openalex.org/W2012371480","https://openalex.org/W2018023106","https://openalex.org/W2022684404","https://openalex.org/W2023088894","https://openalex.org/W2025245059","https://openalex.org/W2035593604","https://openalex.org/W2039366144","https://openalex.org/W2040007132","https://openalex.org/W2043281212","https://openalex.org/W2046331573","https://openalex.org/W2046553535","https://openalex.org/W2048370823","https://openalex.org/W2050871708","https://openalex.org/W2051031503","https://openalex.org/W2052883417","https://openalex.org/W2055500345","https://openalex.org/W2071276955","https://openalex.org/W2072344743","https://openalex.org/W2072373192","https://openalex.org/W2073001881","https://openalex.org/W2075910419","https://openalex.org/W2078895915","https://openalex.org/W2081864922","https://openalex.org/W2083017901","https://openalex.org/W2093487107","https://openalex.org/W2095445700","https://openalex.org/W2117934096","https://openalex.org/W2118587148","https://openalex.org/W2124948346","https://openalex.org/W2126447218","https://openalex.org/W2126800238","https://openalex.org/W2127975978","https://openalex.org/W2129289929","https://openalex.org/W2146095861","https://openalex.org/W2148965913","https://openalex.org/W2150185235","https://openalex.org/W2157883119","https://openalex.org/W2158284238","https://openalex.org/W2164907988","https://openalex.org/W2167018969","https://openalex.org/W2190148340","https://openalex.org/W2256916148","https://openalex.org/W2327420989","https://openalex.org/W2345598951","https://openalex.org/W2550134996","https://openalex.org/W2556342349","https://openalex.org/W2584382407","https://openalex.org/W2608059957","https://openalex.org/W2625995436","https://openalex.org/W2743985642","https://openalex.org/W2758153130","https://openalex.org/W2767170987","https://openalex.org/W2769936938","https://openalex.org/W2810544715","https://openalex.org/W2918085900","https://openalex.org/W2921935427","https://openalex.org/W2950427768","https://openalex.org/W2958410505","https://openalex.org/W2963188648","https://openalex.org/W2963197286","https://openalex.org/W2963491588","https://openalex.org/W2964122806","https://openalex.org/W2964242874","https://openalex.org/W2967488697","https://openalex.org/W2976895931","https://openalex.org/W2978515965","https://openalex.org/W2988325354","https://openalex.org/W2990364650","https://openalex.org/W2994481999","https://openalex.org/W2997339296","https://openalex.org/W3004659881","https://openalex.org/W3008182883","https://openalex.org/W3008455458","https://openalex.org/W3009461225","https://openalex.org/W3012471757","https://openalex.org/W3016144110","https://openalex.org/W3025390840","https://openalex.org/W3028295718","https://openalex.org/W3082030075","https://openalex.org/W3083166268","https://openalex.org/W3083828368","https://openalex.org/W3088799365","https://openalex.org/W3089937487","https://openalex.org/W3098790586","https://openalex.org/W3099042891","https://openalex.org/W3099049924","https://openalex.org/W3099346792","https://openalex.org/W3099661895","https://openalex.org/W3100801504","https://openalex.org/W3103112879","https://openalex.org/W3103392198","https://openalex.org/W3104718096","https://openalex.org/W3106010402","https://openalex.org/W3106187043","https://openalex.org/W3111993716","https://openalex.org/W3115761617","https://openalex.org/W3122911651","https://openalex.org/W3124032619","https://openalex.org/W3124855974","https://openalex.org/W3155163548","https://openalex.org/W3213841907","https://openalex.org/W4214760253","https://openalex.org/W4236109675","https://openalex.org/W4248757863","https://openalex.org/W4297824791","https://openalex.org/W6603255028","https://openalex.org/W6675430651"],"related_works":["https://openalex.org/W4296209631","https://openalex.org/W2561617217","https://openalex.org/W3097449145","https://openalex.org/W4294811468","https://openalex.org/W2355801475","https://openalex.org/W106004901","https://openalex.org/W2170062176","https://openalex.org/W4206911031","https://openalex.org/W2316648939","https://openalex.org/W408992594"],"abstract_inverted_index":{"Abstract":[0],"Backward":[1],"stochastic":[2,15],"differential":[3],"equations":[4,13],"(BSDEs)":[5],"belong":[6],"nowadays":[7],"to":[8,53,60,104,131,228],"the":[9,76,97,106,111,118,121,127,138,147,163,186,218,222,257,262],"most":[10,143],"frequently":[11],"studied":[12],"in":[14,21,75,96,110,117,145,261],"analysis":[16],"and":[17,26,40,44,55,185,244],"computational":[18,124],"stochastics.":[19],"BSDEs":[20,35,116,243],"applications":[22],"are":[23,68],"often":[24],"nonlinear":[25,33,63,85,115],"high-dimensional.":[27],"In":[28],"nearly":[29],"all":[30],"cases":[31],"such":[32],"high-dimensional":[34,64,242],"cannot":[36],"be":[37],"solved":[38],"explicitly":[39],"it":[41],"has":[42,90,101],"been":[43,91,102],"still":[45],"is":[46,221],"a":[47,69,234],"very":[48],"active":[49],"topic":[50],"of":[51,72,108,114,123,126,137,162,217,225,259,265,268],"research":[52,73],"design":[54],"analyze":[56,80],"numerical":[57,81,93,112,128,238,251],"approximation":[58,82,94,113,129,165,239,252],"methods":[59,83],"approximatively":[61,132],"solve":[62],"BSDEs.":[65,269],"Although":[66],"there":[67,89],"large":[70],"number":[71,122],"articles":[74],"scientific":[77,98],"literature":[78,99],"which":[79,100],"for":[84,241],"BSDEs,":[86],"until":[87],"today":[88],"no":[92],"method":[95,130,240,253],"proven":[103],"overcome":[105,229,256],"curse":[107,258],"dimensionality":[109,260],"sense":[119],"that":[120,247],"operations":[125],"compute":[133],"one":[134],"sample":[135],"path":[136],"BSDE":[139],"solution":[140,266],"grows":[141],"at":[142],"polynomially":[144],"both":[146],"reciprocal":[148],"<m:math":[149,167,188],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[150,168,189],"<m:mn>1</m:mn>":[151,202],"<m:mrow>":[152,192,193],"<m:mo>/</m:mo>":[153],"</m:mrow>":[154,196,197],"<m:mi>\u03b5</m:mi>":[155,169],"</m:math>":[156,179,212],"$":[157,161,180,184,213,216],"1":[158],"/":[159],"\\varepsilon":[160,181],"prescribed":[164],"accuracy":[166],"<m:mo>\u2208</m:mo>":[170,191],"<m:mo":[171,177,199,209],"stretchy=\"false\">(</m:mo>":[172],"<m:mn>0</m:mn>":[173],"<m:mo>,</m:mo>":[174,203,205,207],"<m:mi":[175,194],"mathvariant=\"normal\">\u221e</m:mi>":[176],"stretchy=\"false\">)</m:mo>":[178],"\\in(0,":[182],"\\infty)":[183],"dimension":[187],"<m:mi>d</m:mi>":[190],"mathvariant=\"double-struck\">N</m:mi>":[195],"<m:mo>=</m:mo>":[198],"fence=\"false\"":[200,210],"stretchy=\"false\">{</m:mo>":[201],"<m:mn>2</m:mn>":[204],"<m:mn>3</m:mn>":[206],"<m:mo>\u2026</m:mo>":[208],"stretchy=\"false\">}</m:mo>":[211],"d\\in":[214],"{\\mathbb{N}}=\\{1,2,3,\\ldots\\}":[215],"BSDE.":[219],"It":[220],"key":[223],"contribution":[224],"this":[226,230,248],"article":[227],"obstacle":[231],"by":[232,245],"introducing":[233],"new":[235],"Monte":[236,249],"Carlo-type":[237,250],"proving":[246],"does":[254],"indeed":[255],"approximative":[263],"computation":[264],"paths":[267]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
