{"id":"https://openalex.org/W2544379658","doi":"https://doi.org/10.1515/mcma-2016-0115","title":"Approximation of Euler\u2013Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process","display_name":"Approximation of Euler\u2013Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process","publication_year":2016,"publication_date":"2016-10-25","ids":{"openalex":"https://openalex.org/W2544379658","doi":"https://doi.org/10.1515/mcma-2016-0115","mag":"2544379658"},"language":"en","primary_location":{"id":"doi:10.1515/mcma-2016-0115","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2016-0115","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"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":"Monte Carlo Methods and Applications","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/A5070531141","display_name":"Mohsine Benabdallah","orcid":null},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohsine Benabdallah","raw_affiliation_strings":["Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco","institution_ids":["https://openalex.org/I3121676899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083351881","display_name":"Youssfi Elkettani","orcid":null},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Youssfi Elkettani","raw_affiliation_strings":["Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco","institution_ids":["https://openalex.org/I3121676899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045159949","display_name":"Kamal Hiderah","orcid":"https://orcid.org/0000-0002-8165-8685"},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Kamal Hiderah","raw_affiliation_strings":["Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ibn Tofail, 14000 Kenitra, Morocco","institution_ids":["https://openalex.org/I3121676899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045159949"],"corresponding_institution_ids":["https://openalex.org/I3121676899"],"apc_list":null,"apc_paid":null,"fwci":0.4171,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72373285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"4","first_page":"307","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9531999826431274,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9462000131607056,"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/physics","display_name":"Physics","score":0.4948555827140808},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4526127278804779},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45170652866363525},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4442480802536011},{"id":"https://openalex.org/keywords/analytical-chemistry","display_name":"Analytical Chemistry (journal)","score":0.3867137134075165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33745211362838745},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11158353090286255},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.08219391107559204}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4948555827140808},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4526127278804779},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45170652866363525},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4442480802536011},{"id":"https://openalex.org/C113196181","wikidata":"https://www.wikidata.org/wiki/Q485223","display_name":"Analytical Chemistry (journal)","level":2,"score":0.3867137134075165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33745211362838745},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11158353090286255},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08219391107559204},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/mcma-2016-0115","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2016-0115","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"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":"Monte Carlo Methods and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W20060356","https://openalex.org/W162442391","https://openalex.org/W1500844253","https://openalex.org/W1505640237","https://openalex.org/W1534354411","https://openalex.org/W1575104486","https://openalex.org/W1613583603","https://openalex.org/W1626314196","https://openalex.org/W1682752301","https://openalex.org/W1969741290","https://openalex.org/W1972241404","https://openalex.org/W1974091431","https://openalex.org/W1978275259","https://openalex.org/W2000991167","https://openalex.org/W2006367766","https://openalex.org/W2026701194","https://openalex.org/W2029968770","https://openalex.org/W2053606771","https://openalex.org/W2073676861","https://openalex.org/W2087253339","https://openalex.org/W2088463379","https://openalex.org/W2111587503","https://openalex.org/W2136024542","https://openalex.org/W2167963767","https://openalex.org/W2607399731","https://openalex.org/W2617720346","https://openalex.org/W2730656107","https://openalex.org/W3099630887","https://openalex.org/W4231021340","https://openalex.org/W4252343496","https://openalex.org/W4297834176"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,194,215],"consider":[5],"both,":[6],"the":[7,13,22,26,37,50,180,185,196,210,217],"strong":[8,220],"and":[9,165,214],"weak":[10],"convergence":[11,221],"of":[12,25,54,182,198,209,219],"Euler\u2013Maruyama":[14,183,199],"approximation":[15,181,197],"for":[16,184],"one-dimensional":[17,144],"stochastic":[18,51,186],"differential":[19,52,187],"equations":[20,53,188],"involving":[21],"local":[23,38,190],"times":[24],"unknown":[27],"process.":[28],"We":[29,178],"use":[30],"a":[31,143,161,168],"transformation":[32],"in":[33],"order":[34],"to":[35],"remove":[36],"time":[39],"<m:math":[40,56,147,172,200,222],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[41,57,148,173,201,223],"<m:msubsup>":[42,72,126,202,240],"<m:mi>L</m:mi>":[43,127],"<m:mi>t</m:mi>":[44,62,77,128,204],"<m:mi>a</m:mi>":[45,120,129],"</m:msubsup>":[46,78,130,206,244],"</m:math>":[47,137,158,175,207,252],"${L_{t}^{a}}$":[48],"from":[49],"type":[55],"<m:mrow>":[58,59,65,71,79,82,94,104,111,114,117,149,152,224,227,230,234],"<m:msub>":[60,66,85,96,105,235],"<m:mi>X</m:mi>":[61,67,86,203,236,241],"</m:msub>":[63,69,88,99,110,238],"<m:mo>=</m:mo>":[64,226],"<m:mn>0</m:mn>":[68,76],"<m:mo>+</m:mo>":[70,103],"<m:mo":[73,83,89,106,115,122,231,246],"largeop=\"true\"":[74,107],"symmetric=\"true\">\u222b</m:mo>":[75,108],"<m:mi>\u03c6</m:mi>":[80,150],"<m:mo>\u2062</m:mo>":[81,93,113,119,125,229],"stretchy=\"false\">(</m:mo>":[84,116],"<m:mi>s</m:mi>":[87,98],"rspace=\"4.2pt\"":[90],"stretchy=\"false\">)</m:mo>":[91,123],"</m:mrow>":[92,100,101,102,121,124,131,132,133,134,136,156,157,245,249,250,251],"<m:mo>\ud835\udc51</m:mo>":[95],"<m:mi>B</m:mi>":[97],"<m:mi>\u211d</m:mi>":[109,153,155,174],"<m:mi>\u03bd</m:mi>":[112],"<m:mi>d</m:mi>":[118],"<m:mo>.</m:mo>":[135],"$X_{t}=X_{0}+\\int_{0}^{t}\\varphi(X_{s})\\,dB_{s}+\\int_{\\mathbb{R}}\\nu(da)L_{t}^{%":[138],"a}.$":[139],"Here":[140],"B":[141],"is":[142,160,167],"Brownian":[145],"motion,":[146],"<m:mo>:</m:mo>":[151],"<m:mo>\u2192</m:mo>":[154],"${\\varphi:\\mathbb{R}\\rightarrow\\mathbb{R}}$":[159],"bounded":[162,169],"measurable":[163],"function,":[164],"\u03bd":[166],"measure":[170],"on":[171],"${\\mathbb{R}}$":[176],".":[177],"provide":[179,216],"without":[189],"time.":[191],"After":[192],"that,":[193],"conclude":[195],"<m:mi>n</m:mi>":[205,243],"${X_{t}^{n}}$":[208],"above":[211],"mentioned":[212],"equation,":[213],"rate":[218],"<m:mo>Error</m:mo>":[225],"<m:mi>\ud835\udd3c</m:mi>":[228],"fence=\"true\"":[232,247],"stretchy=\"false\">|</m:mo>":[233,248],"<m:mi>T</m:mi>":[237,242],"<m:mo>-</m:mo>":[239],"<jats:inline-grap":[253]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}