{"id":"https://openalex.org/W2016514783","doi":"https://doi.org/10.1109/acc.2014.6859208","title":"A convergence result for the Euler-Maruyama method for a simple stochastic differential equation with discontinuous drift","display_name":"A convergence result for the Euler-Maruyama method for a simple stochastic differential equation with discontinuous drift","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2016514783","doi":"https://doi.org/10.1109/acc.2014.6859208","mag":"2016514783"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2014.6859208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859208","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-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/A5087892124","display_name":"Maria Simonsen","orcid":"https://orcid.org/0000-0003-3460-9132"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Maria Simonsen","raw_affiliation_strings":["[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]"],"affiliations":[{"raw_affiliation_string":"[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077619715","display_name":"Henrik Schi\u00f8ler","orcid":"https://orcid.org/0000-0002-7288-7638"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Henrik Schioler","raw_affiliation_strings":["[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]"],"affiliations":[{"raw_affiliation_string":"[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057662343","display_name":"John Leth","orcid":"https://orcid.org/0000-0001-6043-1687"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"John Leth","raw_affiliation_strings":["[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]"],"affiliations":[{"raw_affiliation_string":"[Dept. of Electron. Syst., Aalborg Univ., Aalborg, Denmark]","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048914092","display_name":"Horia D. Cornean","orcid":"https://orcid.org/0000-0003-2700-8785"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Horia Cornean","raw_affiliation_strings":["[Dept. of Math. Sci., Aalborg Univ., Aalborg, Denmark]"],"affiliations":[{"raw_affiliation_string":"[Dept. of Math. Sci., Aalborg Univ., Aalborg, Denmark]","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087892124"],"corresponding_institution_ids":["https://openalex.org/I891191580"],"apc_list":null,"apc_paid":null,"fwci":1.3753,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84477227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":null,"first_page":"5180","last_page":"5185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"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":0.9991000294685364,"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/T11976","display_name":"Capital Investment and Risk Analysis","score":0.9758999943733215,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7710437774658203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7165995240211487},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.640458881855011},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6090410351753235},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.5964085459709167},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5686473846435547},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5127240419387817},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.511296272277832},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.497163325548172},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.4619790315628052},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4401334226131439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4355359673500061},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41596999764442444},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.4028586745262146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12526962161064148}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7710437774658203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7165995240211487},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.640458881855011},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6090410351753235},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.5964085459709167},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5686473846435547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5127240419387817},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.511296272277832},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.497163325548172},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4619790315628052},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4401334226131439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4355359673500061},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41596999764442444},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.4028586745262146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12526962161064148},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2014.6859208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859208","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:publications/60ecb0c2-469b-4aa5-88e1-bc3222f96575","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/60ecb0c2-469b-4aa5-88e1-bc3222f96575","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Simonsen , M , Schi\u00f8ler , H , Leth , J-J &amp; Cornean , H 2014 , A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift . in American Control Conference (ACC), 2014 . IEEE Press , American Control Conference , pp. 5180 - 5185 , 2014 American Control Conference (ACC) , Portland, OR , United States , 04/06/2014 . https://doi.org/10.1109/ACC.2014.6859208","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W643283668","https://openalex.org/W1515569637","https://openalex.org/W1973376127","https://openalex.org/W2007700189","https://openalex.org/W2008534422","https://openalex.org/W2023462791","https://openalex.org/W2026701194","https://openalex.org/W2029968770","https://openalex.org/W2043496299","https://openalex.org/W2044833311","https://openalex.org/W2130906647","https://openalex.org/W2134426226","https://openalex.org/W2171307019","https://openalex.org/W2423950039","https://openalex.org/W4231021340","https://openalex.org/W6630814712"],"related_works":["https://openalex.org/W2009711572","https://openalex.org/W2365810470","https://openalex.org/W2131733331","https://openalex.org/W2134248673","https://openalex.org/W1674877062","https://openalex.org/W1981367860","https://openalex.org/W2039043967","https://openalex.org/W786968757","https://openalex.org/W4394659182","https://openalex.org/W3153879842"],"abstract_inverted_index":{"The":[0],"Euler-Maruyama":[1,24,69],"method":[2,25],"is":[3,26,36,44,54,84],"applied":[4],"to":[5,74],"a":[6,75,88],"simple":[7],"stochastic":[8],"differential":[9],"equation":[10],"(SDE)":[11],"with":[12,63,87],"discontinuous":[13,64],"drift.":[14],"Convergence":[15],"aspects":[16],"are":[17],"investigated":[18],"in":[19,28,72],"the":[20,23,39,47,58,68,79,92],"case,":[21],"where":[22],"simulated":[27],"dyadic":[29],"points.":[30],"A":[31,81],"strong":[32,76],"rate":[33],"of":[34,57,78],"convergence":[35],"presented":[37,85],"for":[38,61,91],"numerical":[40,82,93],"simulations":[41],"and":[42],"it":[43],"shown":[45],"that":[46,67],"produced":[48],"sequences":[49],"converge":[50,71],"almost":[51],"surely.":[52],"This":[53],"an":[55],"improvement":[56],"general":[59],"result":[60],"SDEs":[62],"drift,":[65],"i.e.":[66],"approximations":[70],"probability":[73],"solution":[77],"SDE.":[80],"example":[83],"together":[86],"confidence":[89],"interval":[90],"solutions.":[94]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
