{"id":"https://openalex.org/W2041537137","doi":"https://doi.org/10.1109/tit.1985.1057036","title":"Large deviations, hypotheses testing, and source coding for finite Markov chains","display_name":"Large deviations, hypotheses testing, and source coding for finite Markov chains","publication_year":1985,"publication_date":"1985-05-01","ids":{"openalex":"https://openalex.org/W2041537137","doi":"https://doi.org/10.1109/tit.1985.1057036","mag":"2041537137"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1985.1057036","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1985.1057036","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/A5027145012","display_name":"S. Natarajan","orcid":"https://orcid.org/0000-0002-8765-1038"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S. Natarajan","raw_affiliation_strings":["Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, India","Statistics and Mathematics Unit Indian Statistical Institute Bangalore India"],"affiliations":[{"raw_affiliation_string":"Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Statistics and Mathematics Unit Indian Statistical Institute Bangalore India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027145012"],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":1.0517,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.75634235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"3","first_page":"360","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9889000058174133,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9889000058174133,"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/T11476","display_name":"Graph theory and applications","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7950723171234131},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.6724814772605896},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6468955278396606},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.6387391090393066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6125674843788147},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5158814191818237},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47466686367988586},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.43326452374458313},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4282546639442444},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4230131506919861},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.4100554585456848},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3878802955150604},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.28738272190093994},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.2700318694114685},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23049592971801758}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7950723171234131},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.6724814772605896},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6468955278396606},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.6387391090393066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6125674843788147},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5158814191818237},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47466686367988586},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.43326452374458313},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4282546639442444},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4230131506919861},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.4100554585456848},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3878802955150604},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.28738272190093994},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.2700318694114685},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23049592971801758}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1985.1057036","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1985.1057036","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1549664537","https://openalex.org/W1596151138","https://openalex.org/W1991315500","https://openalex.org/W2012867143","https://openalex.org/W2024387237","https://openalex.org/W2055094761","https://openalex.org/W2113348989","https://openalex.org/W2165469059","https://openalex.org/W2399816043","https://openalex.org/W4246098931","https://openalex.org/W4300614234"],"related_works":["https://openalex.org/W2800044850","https://openalex.org/W2380835617","https://openalex.org/W1968612088","https://openalex.org/W2734729804","https://openalex.org/W2349429754","https://openalex.org/W2127013863","https://openalex.org/W1189343304","https://openalex.org/W1969706471","https://openalex.org/W2468306076","https://openalex.org/W4379800512"],"abstract_inverted_index":{"Let":[0],"<tex":[1,61],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,62],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{X_{n}\\}":[3],"n":[4],"\\geq":[5],"1</tex>":[6],"be":[7],"a":[8,50],"finite":[9],"Markov":[10],"chain":[11],"with":[12],"transition":[13,29,47],"probability":[14],"matrix":[15,31],"of":[16],"strictly":[17],"positive":[18],"entries.":[19],"A":[20],"large":[21],"deviation":[22],"theorem":[23,59],"is":[24,33,64],"proved":[25],"for":[26,41,60,72],"the":[27,46,52,56,69,73],"empirical":[28],"count":[30],"and":[32,75],"used":[34],"to":[35],"get":[36],"asymptotically":[37],"optimal":[38],"critical":[39],"regions":[40],"testing":[42],"simple":[43],"hypotheses":[44],"about":[45],"matrix.":[48],"As":[49],"corollary,":[51],"error":[53],"exponent":[54],"in":[55],"source":[57],"coding":[58],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{X_{n}\\}</tex>":[63],"obtained.":[65],"These":[66],"results":[67,71],"generalize":[68],"corresponding":[70],"independent":[74],"identically":[76],"distributed":[77],"case.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}
