{"id":"https://openalex.org/W4400295636","doi":"https://doi.org/10.3390/sym16070827","title":"On Asymptotic Equipartition Property for Stationary Process of Moving Averages","display_name":"On Asymptotic Equipartition Property for Stationary Process of Moving Averages","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4400295636","doi":"https://doi.org/10.3390/sym16070827"},"language":"en","primary_location":{"id":"doi:10.3390/sym16070827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070827","pdf_url":"https://www.mdpi.com/2073-8994/16/7/827/pdf?version=1720751042","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/7/827/pdf?version=1720751042","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078825613","display_name":"Yuanyuan Ren","orcid":"https://orcid.org/0000-0001-7802-2128"},"institutions":[{"id":"https://openalex.org/I38756568","display_name":"Xinyang College of Agriculture and Forestry","ror":"https://ror.org/017t6fa07","country_code":"CN","type":"education","lineage":["https://openalex.org/I38756568"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanyuan Ren","raw_affiliation_strings":["School of Mathematics and Statistics, Xinyang College, Xinyang 464000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xinyang College, Xinyang 464000, China","institution_ids":["https://openalex.org/I38756568"]}]},{"author_position":"last","author":{"id":null,"display_name":"Zhongzhi Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I92178344","display_name":"Anhui University of Technology","ror":"https://ror.org/02qdtrq21","country_code":"CN","type":"education","lineage":["https://openalex.org/I92178344"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongzhi Wang","raw_affiliation_strings":["School of Microelectronics and Data Science, Anhui University of Technology, Ma\u2019anshan 243000, China","School of Microelectronics and Data Science, Anhui University of Technology, Ma'anshan 243000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Microelectronics and Data Science, Anhui University of Technology, Ma\u2019anshan 243000, China","institution_ids":["https://openalex.org/I92178344"]},{"raw_affiliation_string":"School of Microelectronics and Data Science, Anhui University of Technology, Ma'anshan 243000, China","institution_ids":["https://openalex.org/I92178344"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078825613"],"corresponding_institution_ids":["https://openalex.org/I38756568"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17799586,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"7","first_page":"827","last_page":"827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9799000024795532,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.6784784197807312},{"id":"https://openalex.org/keywords/equipartition-theorem","display_name":"Equipartition theorem","score":0.6495668888092041},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5644124746322632},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5125608444213867},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5035554766654968},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4985678195953369},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.47814738750457764},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4768049418926239},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.43942195177078247},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41146785020828247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33285191655158997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18495994806289673},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.160920649766922},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11094126105308533},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.10143387317657471},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06878459453582764},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.058312445878982544}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784784197807312},{"id":"https://openalex.org/C99742106","wikidata":"https://www.wikidata.org/wiki/Q255996","display_name":"Equipartition theorem","level":3,"score":0.6495668888092041},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5644124746322632},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5125608444213867},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5035554766654968},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4985678195953369},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47814738750457764},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4768049418926239},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.43942195177078247},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41146785020828247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33285191655158997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18495994806289673},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.160920649766922},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11094126105308533},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.10143387317657471},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06878459453582764},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.058312445878982544},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16070827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070827","pdf_url":"https://www.mdpi.com/2073-8994/16/7/827/pdf?version=1720751042","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b3c0990334814872aa28da3282019fe0","is_oa":false,"landing_page_url":"https://doaj.org/article/b3c0990334814872aa28da3282019fe0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 7, p 827 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16070827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070827","pdf_url":"https://www.mdpi.com/2073-8994/16/7/827/pdf?version=1720751042","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5400000214576721}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321435","display_name":"Anhui University","ror":"https://ror.org/05th6yx34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400295636.pdf","grobid_xml":"https://content.openalex.org/works/W4400295636.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W254342579","https://openalex.org/W1481095752","https://openalex.org/W1968250327","https://openalex.org/W1969661055","https://openalex.org/W1970091448","https://openalex.org/W1991013205","https://openalex.org/W2033672007","https://openalex.org/W2041942465","https://openalex.org/W2049391171","https://openalex.org/W2070532359","https://openalex.org/W2089034314","https://openalex.org/W2478708596","https://openalex.org/W3001016082","https://openalex.org/W3191119384","https://openalex.org/W6648201498"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2090923322","https://openalex.org/W1547993499","https://openalex.org/W2070195754","https://openalex.org/W2142627477","https://openalex.org/W1647946917","https://openalex.org/W2081207015","https://openalex.org/W2072691113","https://openalex.org/W2777849946","https://openalex.org/W2480060391"],"abstract_inverted_index":{"Let":[0],"{Xn}n\u2208Z":[1],"be":[2],"a":[3,9,17,60],"stationary":[4],"process":[5],"with":[6],"values":[7],"in":[8,69,97],"finite":[10],"set.":[11],"In":[12],"this":[13,25,98],"paper,":[14],"we":[15],"present":[16],"moving":[18,42],"average":[19],"version":[20],"of":[21,40,45,72,90],"the":[22,27,35,41,51,74,87],"Shannon\u2013McMillan\u2013Breiman":[23],"theorem;":[24],"generalize":[26],"corresponding":[28],"classical":[29],"results.":[30],"A":[31],"sandwich":[32,62],"argument":[33],"reduced":[34],"proof":[36],"to":[37],"direct":[38],"applications":[39],"strong":[43],"law":[44],"large":[46],"numbers.":[47],"The":[48],"result":[49],"generalizes":[50],"work":[52],"by":[53],"Algoet":[54],"et.":[55],"al.,":[56],"while":[57],"relying":[58],"on":[59],"similar":[61],"method.":[63],"It":[64],"is":[65,92],"worth":[66],"noting":[67],"that,":[68],"some":[70],"kind":[71],"significance,":[73],"indices":[75],"an":[76],"and":[77],"\u03d5(n)":[78],"are":[79],"symmetrical,":[80],"i.e.,":[81],"for":[82],"any":[83],"integer":[84],"n,":[85],"if":[86],"growth":[88],"rate":[89],"(an)n\u2208Z":[91],"slow":[93],"enough,":[94],"all":[95],"conclusions":[96],"article":[99],"still":[100],"hold":[101],"true.":[102]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}