{"id":"https://openalex.org/W2028098276","doi":"https://doi.org/10.1109/tit.1983.1056613","title":"Cycloergodic properties of discrete- parameter nonstationary stochastic processes","display_name":"Cycloergodic properties of discrete- parameter nonstationary stochastic processes","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W2028098276","doi":"https://doi.org/10.1109/tit.1983.1056613","mag":"2028098276"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1983.1056613","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056613","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5032241297","display_name":"Russell A. Boyles","orcid":null},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Boyles","raw_affiliation_strings":["Lawrence Livermore National Laboratory, University of California, Livermore, CA, USA","Lawrence Livermore National Laboratory University of California Livermore CA USA"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory, University of California, Livermore, CA, USA","institution_ids":["https://openalex.org/I1282311441"]},{"raw_affiliation_string":"Lawrence Livermore National Laboratory University of California Livermore CA USA","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051823246","display_name":"William A. Gardner","orcid":"https://orcid.org/0000-0003-3840-7191"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Gardner","raw_affiliation_strings":["Signal and Image Processing Laboratory, Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","[Signal and Image Processing Laboratory, Department of Electrical and Computer Engineering, University of California, Davis, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Laboratory, Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"[Signal and Image Processing Laboratory, Department of Electrical and Computer Engineering, University of California, Davis, CA, USA]","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032241297"],"corresponding_institution_ids":["https://openalex.org/I1282311441"],"apc_list":null,"apc_paid":null,"fwci":2.0649,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.86456996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"29","issue":"1","first_page":"105","last_page":"114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9537000060081482,"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":0.9537000060081482,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9140999913215637,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.8954039812088013},{"id":"https://openalex.org/keywords/cyclostationary-process","display_name":"Cyclostationary process","score":0.8447350263595581},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.6297835111618042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5706222653388977},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5420130491256714},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5022780895233154},{"id":"https://openalex.org/keywords/stationary-ergodic-process","display_name":"Stationary ergodic process","score":0.4948384165763855},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.4528152048587799},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44216835498809814},{"id":"https://openalex.org/keywords/stationary-sequence","display_name":"Stationary sequence","score":0.43676912784576416},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43502986431121826},{"id":"https://openalex.org/keywords/stationary-process","display_name":"Stationary process","score":0.4268070459365845},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39707642793655396},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3625186085700989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3161298632621765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2532489597797394},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1924508512020111},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11494722962379456},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0789271891117096}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8954039812088013},{"id":"https://openalex.org/C178351263","wikidata":"https://www.wikidata.org/wiki/Q3922399","display_name":"Cyclostationary process","level":3,"score":0.8447350263595581},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.6297835111618042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5706222653388977},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5420130491256714},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5022780895233154},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.4948384165763855},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.4528152048587799},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44216835498809814},{"id":"https://openalex.org/C18436578","wikidata":"https://www.wikidata.org/wiki/Q7604346","display_name":"Stationary sequence","level":3,"score":0.43676912784576416},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43502986431121826},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.4268070459365845},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39707642793655396},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3625186085700989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3161298632621765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2532489597797394},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1924508512020111},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11494722962379456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0789271891117096},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1983.1056613","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056613","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W55629925","https://openalex.org/W657967041","https://openalex.org/W1965812785","https://openalex.org/W1975211206","https://openalex.org/W2015360490","https://openalex.org/W2080634882","https://openalex.org/W2084219137","https://openalex.org/W2088809497","https://openalex.org/W2093367443","https://openalex.org/W2154670154","https://openalex.org/W2164861724","https://openalex.org/W2171137293","https://openalex.org/W2914202085","https://openalex.org/W2995875879","https://openalex.org/W4251172797","https://openalex.org/W4285719527","https://openalex.org/W6621838456","https://openalex.org/W6684769486"],"related_works":["https://openalex.org/W4250397825","https://openalex.org/W2523613823","https://openalex.org/W964575223","https://openalex.org/W124275629","https://openalex.org/W2128867967","https://openalex.org/W2532578770","https://openalex.org/W1938186782","https://openalex.org/W4388311358","https://openalex.org/W2209831167","https://openalex.org/W1977915641"],"abstract_inverted_index":{"It":[0],"is":[1,27,70],"shown":[2,28],"that":[3,29],"a":[4],"large":[5],"class":[6],"of":[7,32],"nonstationary":[8],"discrete":[9],"parameter":[10],"stochastic":[11],"processes":[12],"possess":[13],"novel":[14],"ergodic":[15,56],"properties,":[16],"which":[17],"are":[18],"referred":[19],"to":[20],"as":[21],"{\\em":[22],"cycloergodic}":[23],"properties.":[24],"Specifically,":[25],"it":[26],"periodic":[30],"components":[31],"time-varying":[33],"probabilistic":[34],"parameters":[35],"can":[36],"be":[37],"consistently":[38],"estimated":[39],"from":[40],"time":[41],"averages":[42],"on":[43],"one":[44],"sample":[45],"path.":[46],"The":[47],"cycloergodic":[48],"theory":[49,57],"developed":[50],"herein":[51],"extends":[52],"and":[53,62,69,75],"generalizes":[54],"existing":[55],"for":[58],"asymptotically":[59],"mean":[60],"stationary":[61],"<tex":[63],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[64],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</tex>":[65],"-stationary":[66],"(cyclostationary)":[67],"processes,":[68],"presented":[71],"in":[72],"both":[73],"wide-sense":[74],"strict-sense":[76],"contexts.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-05T09:29:38.588285","created_date":"2025-10-10T00:00:00"}