Parameter estimation for uncertain differential equations with small dispersion coefficient

Parameter estimation for uncertain differential equations with small dispersion coefficient | 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 Parameter estimation for uncertain differential equations with small dispersion coefficient Chao Wei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3866163/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Uncertain differential equations (UDEs) are a type of differential equations driven by Liu processes. Statistical inference is a critical issue in the applications of UDEs and scholars have proposed many methods to estimate the unknown parameters. However, the asymptotic properties of the estimators have been discussed in few literature. This paper is concerned with parameter estimation for UDEs with small dispersion coefficient from discrete observations. The least squares estimator is defined, the consistency and asymptotic distribution of estimator are derived. The uncertain Hyperbolic model is provided as analytic example and some numerical examples are given to illustrate the proposed method. MSC Classification : 60G52 , 62F12 Least squares estimation (LSE) uncertain differential equations Liu process consistency asymptotic distribution Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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-3866163","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267747395,"identity":"3f3c2048-8998-42ae-86be-40101d6df3ff","order_by":0,"name":"Chao Wei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYPACNh5+ZuaDD4hUzQzRItnOlmxAihYGBoPzPGYCRGngn5F/8HHBLz4Z48MMZgwMNTbRBLVI3EhmNp7Zx8Zjdpgh7QHDsbTcBoJ6biSzSfP2gLUcN2BsOExYizxMi3EzY5sEUVoMQFp4frDxGDAzsxGnxfDMY2Nj3gY2HonDbMwGCcT4Re544sPHPH+O2fP3n//44EONDRHeF0hgYGBsOwbhJBBUDgL8B4DEnxqi1I6CUTAKRsEIBQDQOjjNw6NilgAAAABJRU5ErkJggg==","orcid":"","institution":"Anyang Normal University","correspondingAuthor":true,"prefix":"","firstName":"Chao","middleName":"","lastName":"Wei","suffix":""}],"badges":[],"createdAt":"2024-01-15 10:29:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3866163/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3866163/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50720028,"identity":"3f6f6691-2b35-4ffc-9c3b-d942df414f0d","added_by":"auto","created_at":"2024-02-06 09:37:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":268332,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3866163/v1_covered_bb282736-737a-41dd-9021-631a237deab9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Parameter estimation for uncertain differential equations with small dispersion coefficient","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":"Least squares estimation (LSE), uncertain differential equations, Liu process, consistency, asymptotic distribution","lastPublishedDoi":"10.21203/rs.3.rs-3866163/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3866163/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUncertain differential equations (UDEs) are a type of differential equations driven by Liu processes. 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