{"id":"https://openalex.org/W2001035714","doi":"https://doi.org/10.1112/s1461157013000120","title":"Weak approximation of stochastic differential delay equations for bounded measurable function","display_name":"Weak approximation of stochastic differential delay equations for bounded measurable function","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2001035714","doi":"https://doi.org/10.1112/s1461157013000120","mag":"2001035714"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157013000120","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157013000120","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A23B1E0E46C8AF14CC5C55AEAA41A311/S1461157013000120a.pdf/div-class-title-weak-approximation-of-stochastic-differential-delay-equations-for-bounded-measurable-function-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A23B1E0E46C8AF14CC5C55AEAA41A311/S1461157013000120a.pdf/div-class-title-weak-approximation-of-stochastic-differential-delay-equations-for-bounded-measurable-function-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100408656","display_name":"Hua Zhang","orcid":"https://orcid.org/0000-0001-6856-1187"},"institutions":[{"id":"https://openalex.org/I59649739","display_name":"Jiangxi University of Finance and Economics","ror":"https://ror.org/03efmyj29","country_code":"CN","type":"education","lineage":["https://openalex.org/I59649739"]},{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hua Zhang","raw_affiliation_strings":["School of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou, Guangdong 510275, PR China email","School of Statistics,Jiangxi University of Finance and Economics,Nanchang, Jiangxi 330013, PR China email","School of Statistics,Jiangxi University of Finance and Economics,Nanchang,Jiangxi 330013,PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou, Guangdong 510275, PR China email","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Statistics,Jiangxi University of Finance and Economics,Nanchang, Jiangxi 330013, PR China email","institution_ids":["https://openalex.org/I59649739"]},{"raw_affiliation_string":"School of Statistics,Jiangxi University of Finance and Economics,Nanchang,Jiangxi 330013,PR China","institution_ids":["https://openalex.org/I59649739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100408656"],"corresponding_institution_ids":["https://openalex.org/I157773358","https://openalex.org/I59649739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.14682011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":null,"first_page":"319","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9961000084877014,"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":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8628122806549072},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7715834379196167},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6500328183174133},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5326010584831238},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.5176635384559631},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5083274245262146},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4731622338294983},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.4699160158634186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4509640336036682},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4227745831012726},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3751492202281952},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3648557960987091}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8628122806549072},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7715834379196167},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6500328183174133},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5326010584831238},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.5176635384559631},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5083274245262146},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4731622338294983},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.4699160158634186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4509640336036682},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4227745831012726},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3751492202281952},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3648557960987091},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157013000120","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157013000120","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A23B1E0E46C8AF14CC5C55AEAA41A311/S1461157013000120a.pdf/div-class-title-weak-approximation-of-stochastic-differential-delay-equations-for-bounded-measurable-function-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157013000120","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157013000120","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A23B1E0E46C8AF14CC5C55AEAA41A311/S1461157013000120a.pdf/div-class-title-weak-approximation-of-stochastic-differential-delay-equations-for-bounded-measurable-function-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1477544716","display_name":null,"funder_award_id":"Guangdong","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1602692349","display_name":null,"funder_award_id":"201204","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2269578665","display_name":null,"funder_award_id":"11171358","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3214160367","display_name":null,"funder_award_id":"No. 11","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3371927120","display_name":"Windows on the Universe: Study of Open Quantum Systems in Atomic Nuclei","funder_award_id":"2012040","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5167091242","display_name":null,"funder_award_id":"No. 1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2001035714.pdf","grobid_xml":"https://content.openalex.org/works/W2001035714.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W571819255","https://openalex.org/W1505057802","https://openalex.org/W1510833486","https://openalex.org/W1969479518","https://openalex.org/W2000262354","https://openalex.org/W2018519672","https://openalex.org/W2022273243","https://openalex.org/W2077315519","https://openalex.org/W2310453869","https://openalex.org/W2527294977","https://openalex.org/W2607399731","https://openalex.org/W2798185321","https://openalex.org/W3098623552","https://openalex.org/W3123242758","https://openalex.org/W4243961535"],"related_works":["https://openalex.org/W4285244990","https://openalex.org/W2014101124","https://openalex.org/W2061383526","https://openalex.org/W4316143821","https://openalex.org/W4361230184","https://openalex.org/W4226238329","https://openalex.org/W1981041832","https://openalex.org/W2509450698","https://openalex.org/W2329156183","https://openalex.org/W2000348976"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,82],"study":[5],"the":[6,22,35,53,71,85],"weak":[7,75],"approximation":[8],"problem":[9],"of":[10,24,52,77],"$E[\\phi":[11,15],"(x(T))]":[12],"$":[13,17,43,91],"by":[14,34],"(y(T))]":[16],",":[18,44],"where":[19],"$x(T)$":[20],"is":[21,32,92],"solution":[23],"a":[25],"stochastic":[26,57],"differential":[27,58],"delay":[28,59],"equation":[29],"and":[30,48,98],"$y(T)$":[31],"defined":[33],"Euler":[36,54,72],"scheme.":[37],"For":[38],"$\\phi":[39,90],"\\in":[40],"{":[41],"C}_{b}^{3}":[42],"Buckwar,":[45],"Kuske,":[46],"Mohammed":[47],"Shardlow":[49],"(\u2018Weak":[50],"convergence":[51,78],"scheme":[55,73],"for":[56],"equations\u2019,":[60],"LMS":[61],"J.":[62],"Comput.":[63],"Math.":[64],"11":[65],"(2008)":[66],"60\u201369)":[67],"have":[68],"shown":[69],"that":[70,84],"has":[74],"order":[76],"$1$":[79],".":[80],"Here":[81],"prove":[83],"same":[86],"results":[87],"hold":[88],"when":[89],"only":[93],"assumed":[94],"to":[95],"be":[96],"measurable":[97],"bounded":[99],"under":[100],"an":[101],"additional":[102],"non-degeneracy":[103],"condition.":[104]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
