{"id":"https://openalex.org/W2158226937","doi":"https://doi.org/10.1142/s021848851100699x","title":"NONSTANDARD CENTRAL LIMIT THEOREMS FOR MARKOV CHAINS","display_name":"NONSTANDARD CENTRAL LIMIT THEOREMS FOR MARKOV CHAINS","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W2158226937","doi":"https://doi.org/10.1142/s021848851100699x","mag":"2158226937"},"language":"en","primary_location":{"id":"doi:10.1142/s021848851100699x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021848851100699x","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","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/A5059326895","display_name":"Bernardo Borba de Andrade","orcid":"https://orcid.org/0000-0003-4688-9733"},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"BERNARDO B. DE ANDRADE","raw_affiliation_strings":["Departamento de Estat\u00edstica \u2013 CCET, Universidade Federal do Rio Grande do Norte, Natal \u2013 RN 59078-970, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Estat\u00edstica \u2013 CCET, Universidade Federal do Rio Grande do Norte, Natal \u2013 RN 59078-970, Brazil","institution_ids":["https://openalex.org/I35046152"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109224432","display_name":"Charles J. Geyer","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CHARLES J. GEYER","raw_affiliation_strings":["School of Statistics, University of Minnesota, 224 Church Street, Minneapolis, MN 55455, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics, University of Minnesota, 224 Church Street, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.20528626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"02","first_page":"251","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9968000054359436,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9968000054359436,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9837999939918518,"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/T13500","display_name":"Probability and Statistical Research","score":0.9828000068664551,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.9132935404777527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8124362230300903},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7746279835700989},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.6137182116508484},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5826190710067749},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.5367468595504761},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.5226566195487976},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4905549883842468},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4797893166542053},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.46016594767570496},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.43426308035850525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.423740953207016},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38709598779678345},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.36833447217941284},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3126642405986786},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.20690971612930298},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.16648313403129578},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13228479027748108},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0888693630695343},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05418407917022705}],"concepts":[{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.9132935404777527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8124362230300903},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7746279835700989},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.6137182116508484},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5826190710067749},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.5367468595504761},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.5226566195487976},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4905549883842468},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4797893166542053},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.46016594767570496},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.43426308035850525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.423740953207016},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38709598779678345},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.36833447217941284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3126642405986786},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.20690971612930298},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.16648313403129578},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13228479027748108},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0888693630695343},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05418407917022705}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021848851100699x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021848851100699x","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[{"id":"https://openalex.org/F4320326287","display_name":"Funda\u00e7\u00e3o de Empreendimentos Cient\u00edficos e Tecnol\u00f3gicos","ror":"https://ror.org/017z2hs09"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W107938046","https://openalex.org/W574059518","https://openalex.org/W624860023","https://openalex.org/W1508700758","https://openalex.org/W1523228994","https://openalex.org/W1535681442","https://openalex.org/W1536597715","https://openalex.org/W1538160166","https://openalex.org/W1963871908","https://openalex.org/W1987805535","https://openalex.org/W1995713768","https://openalex.org/W2001399203","https://openalex.org/W2012497542","https://openalex.org/W2034258817","https://openalex.org/W2036257553","https://openalex.org/W2048971218","https://openalex.org/W2056099894","https://openalex.org/W2057565703","https://openalex.org/W2067914884","https://openalex.org/W2069787050","https://openalex.org/W2073358026","https://openalex.org/W2075525708","https://openalex.org/W2100967164","https://openalex.org/W2106606323","https://openalex.org/W2106706098","https://openalex.org/W2136796925","https://openalex.org/W2146764432","https://openalex.org/W2335062971","https://openalex.org/W2564836637","https://openalex.org/W2578907332","https://openalex.org/W3123857276","https://openalex.org/W3144490774","https://openalex.org/W3203656432","https://openalex.org/W4232076615","https://openalex.org/W4302097244","https://openalex.org/W4302114916"],"related_works":["https://openalex.org/W2110609898","https://openalex.org/W2051268078","https://openalex.org/W2033571578","https://openalex.org/W2312396112","https://openalex.org/W2075860494","https://openalex.org/W2091522449","https://openalex.org/W2986907754","https://openalex.org/W4299281095","https://openalex.org/W3134426083","https://openalex.org/W292716529"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,28,38],"nonstandard":[3,29,56],"central":[4,32,58],"limit":[5,33,59],"theorem":[6,60],"for":[7],"strongly":[8],"mixing":[9],"stationary":[10],"sequences":[11],"using":[12],"the":[13,49,71],"\"radically":[14],"elementary\"":[15],"probability":[16],"theory":[17],"developed":[18],"by":[19],"Nelson":[20],"(1987)":[21],"and":[22],"use":[23],"this":[24],"result":[25],"to":[26,44,47,67],"obtain":[27,48],"Markov":[30,54],"chain":[31,55],"theorem.":[34],"An":[35],"analogue":[36],"of":[37,51,70],"Gaussian":[39],"autoregressive":[40],"process":[41],"is":[42,61],"used":[43],"illustrate":[45],"how":[46],"rate":[50],"convergence.":[52],"A":[53],"functional":[57],"also":[62],"proved":[63],"under":[64],"conditions":[65],"similar":[66],"square":[68],"integrability":[69],"underlying":[72],"martingale.":[73]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
