{"id":"https://openalex.org/W2142979439","doi":"https://doi.org/10.1109/acc.2007.4283151","title":"Some Stochastic Systems with a Fractional Brownian Motion and Applications to Control","display_name":"Some Stochastic Systems with a Fractional Brownian Motion and Applications to Control","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2142979439","doi":"https://doi.org/10.1109/acc.2007.4283151","mag":"2142979439"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4283151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4283151","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 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/A5054666993","display_name":"Tyrone E. Duncan","orcid":"https://orcid.org/0000-0002-6664-9967"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. E. Duncan","raw_affiliation_strings":["Faculty of Department of Mathematics, University of Kansas, Lawrence, KS, USA","University of Kansas LAWRENCE"],"affiliations":[{"raw_affiliation_string":"Faculty of Department of Mathematics, University of Kansas, Lawrence, KS, USA","institution_ids":["https://openalex.org/I146416000"]},{"raw_affiliation_string":"University of Kansas LAWRENCE","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054666993"],"corresponding_institution_ids":["https://openalex.org/I146416000"],"apc_list":null,"apc_paid":null,"fwci":1.9789,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86021505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":null,"first_page":"1110","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9929999709129333,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.8860345482826233},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"Geometric Brownian motion","score":0.8017409443855286},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6753479838371277},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6751384735107422},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.6538585424423218},{"id":"https://openalex.org/keywords/brownian-excursion","display_name":"Brownian excursion","score":0.5859787464141846},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.48947107791900635},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.45946288108825684},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.45422226190567017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4513305127620697},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4429120421409607},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.4339887499809265},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4223238527774811},{"id":"https://openalex.org/keywords/reflected-brownian-motion","display_name":"Reflected Brownian motion","score":0.4170565605163574},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3274519443511963},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30100277066230774},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14875540137290955}],"concepts":[{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.8860345482826233},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.8017409443855286},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6753479838371277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6751384735107422},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6538585424423218},{"id":"https://openalex.org/C53920899","wikidata":"https://www.wikidata.org/wiki/Q4976524","display_name":"Brownian excursion","level":5,"score":0.5859787464141846},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.48947107791900635},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.45946288108825684},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.45422226190567017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4513305127620697},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4429120421409607},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.4339887499809265},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4223238527774811},{"id":"https://openalex.org/C116779161","wikidata":"https://www.wikidata.org/wiki/Q7307228","display_name":"Reflected Brownian motion","level":5,"score":0.4170565605163574},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3274519443511963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30100277066230774},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14875540137290955},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","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":1,"locations":[{"id":"doi:10.1109/acc.2007.4283151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4283151","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W205726716","https://openalex.org/W1964927673","https://openalex.org/W1970943856","https://openalex.org/W1971200514","https://openalex.org/W1973604362","https://openalex.org/W1995998075","https://openalex.org/W2003490810","https://openalex.org/W2028295625","https://openalex.org/W2029774109","https://openalex.org/W2031753087","https://openalex.org/W2039655644","https://openalex.org/W2040337767","https://openalex.org/W2076209196","https://openalex.org/W2079073804","https://openalex.org/W2083731191","https://openalex.org/W2094649962","https://openalex.org/W2122853444","https://openalex.org/W2127436039","https://openalex.org/W2140275726","https://openalex.org/W2180071254","https://openalex.org/W2341760625","https://openalex.org/W3125246470","https://openalex.org/W4246833055","https://openalex.org/W4248995214","https://openalex.org/W4389943602","https://openalex.org/W6704461345"],"related_works":["https://openalex.org/W4386755294","https://openalex.org/W1982823440","https://openalex.org/W4312743876","https://openalex.org/W2003596454","https://openalex.org/W4382939522","https://openalex.org/W2054691066","https://openalex.org/W2058380216","https://openalex.org/W2393106323","https://openalex.org/W2375736556","https://openalex.org/W4301683645"],"abstract_inverted_index":{"In":[0],"this":[1,99],"paper":[2],"some":[3],"stochastic":[4,12,59,81],"systems":[5],"are":[6,9],"considered":[7],"that":[8],"described":[10],"by":[11,30,41],"differential":[13,60],"equations":[14],"with":[15,62,84],"a":[16,23,31,37,42,53,57,63,80],"fractional":[17,38,64,87],"Brownian":[18,39,65,88],"motion.":[19],"The":[20,94],"notion":[21],"of":[22,33,72],"weak":[24,46],"solution":[25,47],"is":[26,49,90,101],"introduced":[27],"and":[28,67,92],"obtained":[29],"transformation":[32],"the":[34,70],"measure":[35],"for":[36,56,79],"motion":[40,66,89],"Radon-Nikodym":[43],"derivative.":[44],"This":[45],"approach":[48],"used":[50],"to":[51,68],"solve":[52],"control":[54],"problem":[55,78,100],"controlled":[58],"equation":[61],"verify":[69],"existence":[71],"an":[73,85],"optimal":[74],"control.":[75],"An":[76],"estimation":[77],"signal":[82],"observed":[83],"additive":[86],"formulated":[91],"solved.":[93],"conditional":[95],"expectation":[96],"which":[97],"solves":[98],"exhibited":[102],"explicitly.":[103]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}