{"id":"https://openalex.org/W1540042060","doi":"https://doi.org/10.3233/rda-2009-0013","title":"Some topics in fractional Brownian motion","display_name":"Some topics in fractional Brownian motion","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1540042060","doi":"https://doi.org/10.3233/rda-2009-0013","mag":"1540042060"},"language":"en","primary_location":{"id":"doi:10.3233/rda-2009-0013","is_oa":false,"landing_page_url":"https://doi.org/10.3233/rda-2009-0013","pdf_url":null,"source":{"id":"https://openalex.org/S2764680446","display_name":"Risk and Decision Analysis","issn_l":"1569-7371","issn":["1569-7371","1875-9173"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Risk and Decision Analysis","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/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":"Tyrone E. Duncan","raw_affiliation_strings":["University of Kansas"],"affiliations":[{"raw_affiliation_string":"University of Kansas","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":0.7844,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82264983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"1","issue":"3","first_page":"145","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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":0.9944000244140625,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9606000185012817,"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/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.6002581119537354},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.45909982919692993},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3239370882511139},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3217860460281372},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28795158863067627},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07583534717559814}],"concepts":[{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.6002581119537354},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.45909982919692993},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3239370882511139},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3217860460281372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28795158863067627},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07583534717559814}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/rda-2009-0013","is_oa":false,"landing_page_url":"https://doi.org/10.3233/rda-2009-0013","pdf_url":null,"source":{"id":"https://openalex.org/S2764680446","display_name":"Risk and Decision Analysis","issn_l":"1569-7371","issn":["1569-7371","1875-9173"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Risk and Decision Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W205726716","https://openalex.org/W1554577510","https://openalex.org/W1969375897","https://openalex.org/W1970943856","https://openalex.org/W1995998075","https://openalex.org/W1998167411","https://openalex.org/W2003427294","https://openalex.org/W2005200870","https://openalex.org/W2031753087","https://openalex.org/W2061630179","https://openalex.org/W2074366794","https://openalex.org/W2076209196","https://openalex.org/W2083731191","https://openalex.org/W2088581336","https://openalex.org/W2101763025","https://openalex.org/W2104833127","https://openalex.org/W2105818147","https://openalex.org/W2122725377","https://openalex.org/W2122853444","https://openalex.org/W2128796442","https://openalex.org/W2161798353","https://openalex.org/W2180071254","https://openalex.org/W2979559266","https://openalex.org/W3212303547"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2373202200","https://openalex.org/W2753870633","https://openalex.org/W4321513530","https://openalex.org/W2165241701","https://openalex.org/W3021897514","https://openalex.org/W1573173092","https://openalex.org/W2950151750","https://openalex.org/W3034439966","https://openalex.org/W2960646972"],"abstract_inverted_index":{"Fractional":[0,265],"Brownian":[1,88,172,188,219,229,248,266],"motion":[2,189,230,267],"denotes":[3],"a":[4,16,58,69,148,227],"family":[5,85],"of":[6,19,86,94,129,135,155,168,217,246],"Gaussian":[7,117],"processes":[8,28,45,56,111,118,131,200],"whose":[9],"applicability":[10],"has":[11,231],"been":[12,47],"demonstrated":[13],"empirically":[14,124,194],"for":[15,39,71,109,198,224,243],"wide":[17],"variety":[18],"physical":[20,34],"phenomena.":[21],"For":[22],"more":[23,40],"than":[24,41],"five":[25],"decades,":[26],"these":[27,44,110,130,199],"have":[29,46,57],"described":[30],"risky":[31],"outcomes":[32],"or":[33,60,159],"uncertainties":[35],"and":[36,77,115,190,209,236,261],"in":[37,52,63,132,137,144,233],"particular":[38],"four":[42],"decades":[43],"used":[48],"to":[49,174,255],"model":[50,70,175],"fluctuations":[51],"economic":[53,176],"data.":[54],"These":[55],"selfsimilarity":[59],"fractal":[61],"property":[62],"probability":[64],"law.":[65],"They":[66],"can":[67,119],"provide":[68],"long":[72,153],"range":[73],"dependence,":[74],"rare":[75],"events":[76],"bursty":[78,149],"behavior.":[79],"Kolmogorov":[80],"[15]":[81],"initially":[82],"defined":[83],"the":[84,106,138,185,205,240,244],"fractional":[87,171,187,218,228,247],"motions":[89,173,249],"motivated":[90,164],"by":[91,103,165],"his":[92,133,166],"study":[93,167],"turbulence":[95,181],"[16,17],":[96],"though":[97],"Schonberg":[98],"[25]":[99],"predated":[100],"Kolmogorov\u2019s":[101],"construction":[102],"showing":[104],"that":[105,192],"covariance":[107],"functions":[108],"are":[112],"positive":[113],"definite":[114],"thereby":[116],"be":[120],"constructed.":[121],"Hurst":[122,193,206],"[14]":[123],"identified":[125],"an":[126,196],"index":[127,197],"parameter":[128],"modeling":[134],"rainfall":[136,143,158],"Nile":[139],"River":[140],"region.":[141],"The":[142,221],"this":[145],"region":[146],"had":[147],"behavior":[150],"with":[151,226],"often":[152],"periods":[154],"either":[156],"excessive":[157],"meager":[160],"rainfall.":[161],"Mandelbrot":[162,208],"[19]":[163],"fractals":[169],"studied":[170],"data":[177],"as":[178,180,251],"well":[179],"[20].":[182],"He":[183],"coined":[184],"name":[186],"noted":[191],"computed":[195],"which":[201],"is":[202],"now":[203],"called":[204],"index.":[207],"van":[210],"Ness":[211],"[21]":[212],"investigated":[213],"some":[214],"basic":[215],"properties":[216],"motion.":[220],"empirical":[222,241],"evidence":[223,242],"models":[225,253],"continued":[232],"hydrology,":[234],"finance":[235],"turbulence.":[237],"More":[238],"recently":[239],"use":[245],"(FBMs)":[250],"random":[252],"broadened":[254],"internet":[256],"traffic":[257],"[4,18],":[258],"medicine":[259],"[23]":[260],"cognition":[262],"[3,12].":[263],"2.":[264]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}