{"id":"https://openalex.org/W2091665787","doi":"https://doi.org/10.1137/130928431","title":"Stochastic Approximation Finite Element Method: Analytical Formulas for Multidimensional Diffusion Process","display_name":"Stochastic Approximation Finite Element Method: Analytical Formulas for Multidimensional Diffusion Process","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2091665787","doi":"https://doi.org/10.1137/130928431","mag":"2091665787"},"language":"en","primary_location":{"id":"doi:10.1137/130928431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130928431","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00842608","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030822806","display_name":"Romain Bompis","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"R. Bompis","raw_affiliation_strings":["Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique"],"affiliations":[{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078591220","display_name":"Emmanuel Gobet","orcid":"https://orcid.org/0000-0002-9940-2493"},"institutions":[{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"E. Gobet","raw_affiliation_strings":["Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique"],"affiliations":[{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030822806"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210107641"],"apc_list":null,"apc_paid":null,"fwci":1.3759,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85207324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"52","issue":"6","first_page":"3140","last_page":"3164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9929999709129333,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5954022407531738},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.5905942916870117},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5721693634986877},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5518720746040344},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.49886393547058105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49330154061317444},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4811059832572937},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48091885447502136},{"id":"https://openalex.org/keywords/heavy-traffic-approximation","display_name":"Heavy traffic approximation","score":0.47690749168395996},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4717565178871155},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4430355727672577},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3801783323287964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24332588911056519},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12216764688491821},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06742879748344421}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5954022407531738},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.5905942916870117},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5721693634986877},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5518720746040344},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.49886393547058105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49330154061317444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4811059832572937},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48091885447502136},{"id":"https://openalex.org/C193290586","wikidata":"https://www.wikidata.org/wiki/Q17022030","display_name":"Heavy traffic approximation","level":2,"score":0.47690749168395996},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4717565178871155},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4430355727672577},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3801783323287964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24332588911056519},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12216764688491821},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06742879748344421},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130928431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130928431","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:CiteSeerX.psu:10.1.1.739.5828","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.739.5828","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/84/26/08/PDF/submitted_multi_dim_final_v2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00842608v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00842608","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Numerical Analysis, 2014, 52 (6), pp.3140-3164. &#x27E8;10.1137/130928431&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00842608v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00842608","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Numerical Analysis, 2014, 52 (6), pp.3140-3164. &#x27E8;10.1137/130928431&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W52263754","https://openalex.org/W632384241","https://openalex.org/W1487597787","https://openalex.org/W1492326914","https://openalex.org/W1554577510","https://openalex.org/W1573874356","https://openalex.org/W1575104486","https://openalex.org/W1576475658","https://openalex.org/W1580561995","https://openalex.org/W1602773783","https://openalex.org/W1966829836","https://openalex.org/W1981151146","https://openalex.org/W1984865765","https://openalex.org/W2017829019","https://openalex.org/W2024591553","https://openalex.org/W2048370823","https://openalex.org/W2076738050","https://openalex.org/W2092264912","https://openalex.org/W2163037328","https://openalex.org/W2314913127","https://openalex.org/W2607399731","https://openalex.org/W2997679055","https://openalex.org/W3105063129","https://openalex.org/W3204708751","https://openalex.org/W4255975175","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1535422765","https://openalex.org/W1964286703","https://openalex.org/W2169866437","https://openalex.org/W4252917280","https://openalex.org/W2137147384","https://openalex.org/W4244850953","https://openalex.org/W2952549193","https://openalex.org/W4253335642","https://openalex.org/W1777598960","https://openalex.org/W2316238076"],"abstract_inverted_index":{"We":[0,47,57],"derive":[1],"an":[2,94],"analytical":[3],"weak":[4],"approximation":[5,52,64],"of":[6,24,31,39,61,77,85,89],"a":[7,35],"multidimensional":[8],"diffusion":[9,33,68],"process":[10,69],"as":[11],"coefficients":[12],"are":[13],"small":[14,102],"or":[15],"time":[16,72],"is":[17,110],"small.":[18],"Our":[19],"methodology":[20],"combines":[21],"the":[22,29,32,40,45,50,67,71,75,78,86],"use":[23],"Gaussian":[25],"proxies":[26],"to":[27,44,98],"approximate":[28],"law":[30],"and":[34,74,103],"finite":[36,53],"element":[37,54],"interpolation":[38],"terminal":[41,79],"function":[42],"applied":[43],"diffusion.":[46],"call":[48],"this":[49],"stochastic":[51],"(SAFE)":[55],"method.":[56],"provide":[58],"error":[59],"bounds":[60],"our":[62,90],"global":[63],"depending":[65],"on":[66],"coefficients,":[70],"horizon,":[73],"regularity":[76],"function.":[80],"Then":[81],"we":[82],"give":[83],"estimates":[84],"computational":[87],"cost":[88],"algorithm.":[91],"This":[92],"shows":[93],"improved":[95],"efficiency":[96],"compared":[97],"Monte-Carlo":[99],"methods":[100],"in":[101],"medium":[104],"dimensions":[105],"(smaller":[106],"than":[107],"10),":[108],"which":[109],"confirmed":[111],"by":[112],"numerical":[113],"experiments.":[114]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
