The Generalized AEP for Higher Order Nonhomogeneous Markov Information Source

The Generalized AEP for Higher Order Nonhomogeneous Markov Information Source | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Generalized AEP for Higher Order Nonhomogeneous Markov Information Source Lyu Bai, Zhiyan Shi, Xiaoyu Zhu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3343679/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract The asymptotic equipartiton property (AEP) plays a crucial role in information theory, providing a theoretical foundation for understanding and analyzing aspects such as coding, compression, and the reliability of communication systems. In this paper, we mainly study the generalized AEP of higher order nonhomogeneous Markov information sources by establishing several strong deviation theorems. To achieve this, we first introduce the concepts of generalized sample divergence rate of th-order nonhomogeneous Markov information sources. Meanwhile, we give a class of generalized strong deviation theorems for moving average of the functions of + 1 variables for th-order nonhomogeneous Markov information sources, and also establish strong deviation theorems and strong limit theorems of the frequencies of occurrence of ordered tuples of states for this Markov information sources. Finally, the generalized AEP for th-order nonhomogeneous Markov information sources are establised. Our results also generalize some known results. MSC(2020): 60J10; 60F15; 94A15 Markov information sources strong deviation theorems AEP Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3343679","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267396121,"identity":"74964eef-dddb-4a8b-b703-feddcd009df0","order_by":0,"name":"Lyu Bai","email":"","orcid":"","institution":"School of Finance \u0026 Economics,Jiangsu University","correspondingAuthor":false,"prefix":"","firstName":"Lyu","middleName":"","lastName":"Bai","suffix":""},{"id":233592055,"identity":"0416bc5a-ebf9-4a45-b284-65da8b9ad636","order_by":1,"name":"Zhiyan Shi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIie2Rv0oDQRCH9xjZNAtp5wh4rzCycImI+CzLFWkski6CxJUFW9sTxWdYEAJ2hgErwfYEi5x5hLQKrtpY3aYU3K/6FfMN80eIROIvgpkFQSEALFc4w93+9kpPVjR6GuncRpXQ/zv0VYknFzPjY0px7dxmMuFiCErTyy1mXkD71nQo9Lq0uibeu3dy2l4tEIZCan3cpaCxlSLOPMOdzhco962Sgy6lqI3loBx5FuXg4wYVPUQU0ZhzFxTjeafE3CJGFWqMA0XjynM4Mj4i5S6yS1GP1xv1fnDonzm88nR+dtlz7bpzsB/crwzx8i/m25UlEonE/+QTkGxK3CvwdLsAAAAASUVORK5CYII=","orcid":"","institution":"Jiangsu University","correspondingAuthor":true,"prefix":"","firstName":"Zhiyan","middleName":"","lastName":"Shi","suffix":""},{"id":233592056,"identity":"c0a42511-d0f9-4250-81d5-3180962b3888","order_by":2,"name":"Xiaoyu Zhu","email":"","orcid":"","institution":"Jiangsu University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Zhu","suffix":""}],"badges":[],"createdAt":"2023-09-11 06:44:31","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-3343679/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-3343679/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49713900,"identity":"c76c6256-d5aa-4f2a-8101-4565df858de7","added_by":"auto","created_at":"2024-01-16 20:44:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":270790,"visible":true,"origin":"","legend":"","description":"","filename":"stochastic.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3343679/v2_covered_e815c129-d18c-4542-8f2a-3e04c81c5903.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"The Generalized AEP for Higher Order Nonhomogeneous Markov Information Source","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Markov information sources, strong deviation theorems, AEP","lastPublishedDoi":"10.21203/rs.3.rs-3343679/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3343679/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe asymptotic equipartiton property (AEP) plays a crucial role in information theory, providing a theoretical foundation for understanding and analyzing aspects such as coding, compression, and the reliability of communication systems. In this paper, we mainly study the generalized AEP of higher order nonhomogeneous Markov information sources by establishing several strong deviation theorems. To achieve this, we first introduce the concepts of generalized sample divergence rate of th-order nonhomogeneous Markov information sources. Meanwhile, we give a class of generalized strong deviation theorems for moving average of the functions of + 1 variables for th-order nonhomogeneous Markov information sources, and also establish strong deviation theorems and strong limit theorems of the frequencies of occurrence of ordered tuples of states for this Markov information sources. Finally, the generalized AEP for th-order nonhomogeneous Markov information sources are establised. 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