{"id":"https://openalex.org/W1987253195","doi":"https://doi.org/10.1137/030601429","title":"Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise","display_name":"Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1987253195","doi":"https://doi.org/10.1137/030601429","mag":"1987253195"},"language":"en","primary_location":{"id":"doi:10.1137/030601429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601429","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.18452/2606","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087450694","display_name":"Werner R\u00f6misch","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Werner R\u00f6misch","raw_affiliation_strings":["Humboldt-Universit\u00e4t Berlin Institut f\u00fcr Mathematik 10099 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Humboldt-Universit\u00e4t Berlin Institut f\u00fcr Mathematik 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045353301","display_name":"Renate Winkler","orcid":"https://orcid.org/0000-0003-2698-3060"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Renate Winkler","raw_affiliation_strings":["Humboldt-Universit\u00e4t Berlin Institut f\u00fcr Mathematik 10099 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Humboldt-Universit\u00e4t Berlin Institut f\u00fcr Mathematik 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087450694"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":7.7937,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.97125138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"28","issue":"2","first_page":"604","last_page":"625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9958999752998352,"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":0.9958999752998352,"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/T11195","display_name":"Simulation Techniques and Applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.8334805965423584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.802553117275238},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5718504190444946},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5412752628326416},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5062681436538696},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4976251423358917},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4769127070903778},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.4654442071914673},{"id":"https://openalex.org/keywords/adaptive-stepsize","display_name":"Adaptive stepsize","score":0.4511394798755646},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4450600743293762},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4283279776573181},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39779311418533325},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.3656122088432312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11779552698135376},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09445428848266602}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.8334805965423584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.802553117275238},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5718504190444946},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5412752628326416},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5062681436538696},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4976251423358917},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4769127070903778},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4654442071914673},{"id":"https://openalex.org/C48077252","wikidata":"https://www.wikidata.org/wiki/Q4680766","display_name":"Adaptive stepsize","level":3,"score":0.4511394798755646},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4450600743293762},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4283279776573181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39779311418533325},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.3656122088432312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11779552698135376},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09445428848266602},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/030601429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601429","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.141.4576","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.4576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-iam.mathematik.hu-berlin.de/~romisch/papers/60142.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.hu-berlin.de:18452/3258","is_oa":false,"landing_page_url":"http://edoc.hu-berlin.de/18452/3258","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"book"},{"id":"doi:10.18452/2606","is_oa":true,"landing_page_url":"https://doi.org/10.18452/2606","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.18452/2606","is_oa":true,"landing_page_url":"https://doi.org/10.18452/2606","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W112910089","https://openalex.org/W194549626","https://openalex.org/W1179040237","https://openalex.org/W1275718198","https://openalex.org/W1500790902","https://openalex.org/W1554532768","https://openalex.org/W1575104486","https://openalex.org/W1988884493","https://openalex.org/W2018810732","https://openalex.org/W2019795760","https://openalex.org/W2021426723","https://openalex.org/W2028572928","https://openalex.org/W2033874189","https://openalex.org/W2042467745","https://openalex.org/W2064362425","https://openalex.org/W2073937734","https://openalex.org/W2085672697","https://openalex.org/W2107995041","https://openalex.org/W2122771530","https://openalex.org/W2130384279","https://openalex.org/W2131821335","https://openalex.org/W2160546858","https://openalex.org/W2268756671","https://openalex.org/W2273042966","https://openalex.org/W3209416867","https://openalex.org/W4231021340","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2189596786","https://openalex.org/W4382053489","https://openalex.org/W2089955609","https://openalex.org/W2039299714","https://openalex.org/W2466040413","https://openalex.org/W4383710307","https://openalex.org/W4307700932","https://openalex.org/W2290376096","https://openalex.org/W2276868677","https://openalex.org/W2887130266"],"abstract_inverted_index":{"A":[0],"strategy":[1,29,71],"for":[2,37,47,56,74,81],"controlling":[3],"the":[4,7,22,42,57,61,70],"stepsize":[5,32],"in":[6],"numerical":[8],"integration":[9],"of":[10,25,44,60,64],"stochastic":[11,89],"differential":[12],"equations":[13],"(SDEs)":[14],"is":[15,18,79],"presented.":[16],"It":[17],"based":[19],"on":[20],"estimating":[21],"pth":[23,62],"mean":[24,63],"local":[26,65],"errors.":[27],"The":[28],"leads":[30],"to":[31],"sequences":[33],"that":[34,69],"are":[35],"identical":[36],"all":[38],"computed":[39],"paths.":[40],"For":[41],"family":[43],"Euler":[45],"schemes":[46],"SDEs":[48,86],"with":[49],"small":[50],"noise,":[51],"we":[52],"derive":[53],"computable":[54],"estimates":[55],"dominating":[58],"term":[59],"errors":[66],"and":[67,87],"show":[68],"becomes":[72],"efficient":[73],"reasonable":[75],"stepsizes.":[76],"Numerical":[77],"experience":[78],"reported":[80],"test":[82],"examples":[83],"including":[84],"scalar":[85],"a":[88],"circuit":[90],"model.":[91]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}