{"id":"https://openalex.org/W1557014342","doi":"https://doi.org/10.1007/978-0-387-35579-5_5","title":"Maximum Likelihood Estimation of the Parameters of Fractional Brownian Traffic with Geometrical Sampling","display_name":"Maximum Likelihood Estimation of the Parameters of Fractional Brownian Traffic with Geometrical Sampling","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1557014342","doi":"https://doi.org/10.1007/978-0-387-35579-5_5","mag":"1557014342"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-35579-5_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35579-5_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-35579-5_5.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Broadband Communications","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-35579-5_5.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019294699","display_name":"Attila Vid\u00e1cs","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I4210161853","display_name":"Budapest Institute","ror":"https://ror.org/050hvq478","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210161853"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Attila Vid\u00e1cs","raw_affiliation_strings":["High Speed Networks Laboratories Dept. of Telecommunications and Telematics, Technical University of Budapest, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/D, H-1117, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"High Speed Networks Laboratories Dept. of Telecommunications and Telematics, Technical University of Budapest, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/D, H-1117, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109","https://openalex.org/I4210161853"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058639214","display_name":"Jorma Virtamo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jorma T. Virtamo","raw_affiliation_strings":["Lab. of Telecommunications Technology, Helsinki University of Technology, P.O.B. 3000, FIN-02015, HUT, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lab. of Telecommunications Technology, Helsinki University of Technology, P.O.B. 3000, FIN-02015, HUT, Finland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5544,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.91981496,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"51","last_page":"62"},"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":0.9977999925613403,"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":0.9977999925613403,"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":0.9939000010490417,"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":0.9739000201225281,"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":0.7838716506958008},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.7143920660018921},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.660256028175354},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5238580703735352},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.5179221034049988},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.49157604575157166},{"id":"https://openalex.org/keywords/hurst-exponent","display_name":"Hurst exponent","score":0.47881442308425903},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4627203345298767},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4406720995903015},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4357713758945465},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.42487403750419617},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39415836334228516},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.3920797109603882},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1426793932914734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09942886233329773}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7838716506958008},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.7143920660018921},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.660256028175354},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5238580703735352},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5179221034049988},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.49157604575157166},{"id":"https://openalex.org/C96835011","wikidata":"https://www.wikidata.org/wiki/Q1638718","display_name":"Hurst exponent","level":2,"score":0.47881442308425903},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4627203345298767},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4406720995903015},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4357713758945465},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.42487403750419617},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39415836334228516},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.3920797109603882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1426793932914734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09942886233329773},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-0-387-35579-5_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35579-5_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-35579-5_5.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Broadband Communications","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.2682","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.2682","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hsnlab.tmit.bme.hu/~vidacs/publications/bc99.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/978-0-387-35579-5_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35579-5_5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-35579-5_5.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Broadband Communications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1557014342.pdf","grobid_xml":"https://content.openalex.org/works/W1557014342.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1545748428","https://openalex.org/W1978061253","https://openalex.org/W2137764909","https://openalex.org/W2146271801","https://openalex.org/W2319085245","https://openalex.org/W2476889740","https://openalex.org/W2491099598","https://openalex.org/W4252112222"],"related_works":["https://openalex.org/W2915158306","https://openalex.org/W2364010220","https://openalex.org/W26397136","https://openalex.org/W4390827289","https://openalex.org/W3010725710","https://openalex.org/W2401810189","https://openalex.org/W2012792015","https://openalex.org/W2087458835","https://openalex.org/W3001803811","https://openalex.org/W3021897514"],"abstract_inverted_index":{"Traffic":[0],"model":[1],"based":[2],"on":[3,112],"the":[4,12,20,30,40,55,58,63,69,90,94,107,123,135,152,157,160],"fractional":[5],"Brownian":[6],"motion":[7],"(fBm)":[8],"contains":[9],"three":[10],"parameters:":[11],"mean":[13],"rate":[14],"m,":[15],"variance":[16],"parameter":[17,22],"a":[18,81,104,117,164],"and":[19,44,127],"Hurst":[21],"H.":[23],"The":[24,132],"estimation":[25,136],"of":[26,48,75,93,134,159,167],"these":[27],"parameters":[28],"by":[29,103,140],"maximum":[31],"likelihood":[32],"(ML)":[33],"method":[34],"is":[35,66,84,100,110,138],"studied.":[36],"Explicit":[37],"expressions":[38],"for":[39,57,122],"ML":[41],"estimates":[42,145],"m":[43],"\u00e2":[45],"in":[46,86],"terms":[47],"H":[49],"are":[50,130],"given,":[51],"as":[52,54,68],"well":[53],"expression":[56],"log-likelihood":[59],"function":[60],"from":[61],"which":[62],"estimate":[64,161],"\u0124":[65,162],"obtained":[67,146],"maximizing":[70],"argument.":[71],"A":[72],"geometric":[73],"sequence":[74],"sampling":[76,154],"points,":[77],"t":[78],"i":[79,82],"=":[80],",":[83],"introduced":[85],"order":[87],"to":[88,116],"see":[89],"scaling":[91],"behaviour":[92],"traffic":[95,108],"with":[96,143,147,163],"fewer":[97],"samples.":[98,168],"It":[99],"shown":[101],"that":[102,151],"proper":[105],"\u2018descaling\u2019":[106],"process":[109],"stationary":[111],"this":[113],"grid":[114,149],"leading":[115],"Toeplitz-type":[118],"covariance":[119,125],"matrix.":[120],"Approximations":[121],"inverted":[124],"matrix":[126],"its":[128],"determinant":[129],"introduced.":[131],"accuracy":[133,158],"algorithm":[137],"studied":[139],"simulations.":[141],"Comparisons":[142],"corresponding":[144],"linear":[148],"show":[150],"geometrical":[153],"indeed":[155],"improves":[156],"given":[165],"number":[166]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
