Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles

Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles | 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 Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles Hanwu Li, Ning Ning This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4184317/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Mar, 2025 Read the published version in Stochastics and Partial Differential Equations: Analysis and Computations → Version 1 posted 7 You are reading this latest preprint version Abstract In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected G-BSDEs with a lower obstacle that are monotone decreasing. By employing this approach, we establish the well-posedness of the solution of the doubly reflected G-BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time. G-expectation reflected backward SDE nonlinear PDE double obstacles MSC-classification: 60G65 60H10 60H30 Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Mar, 2025 Read the published version in Stochastics and Partial Differential Equations: Analysis and Computations → Version 1 posted Editorial decision: Accepted 06 Feb, 2025 Reviews received at journal 06 Feb, 2025 Reviewers agreed at journal 06 Feb, 2025 Reviewers invited by journal 06 Feb, 2025 Submission checks completed at journal 29 Mar, 2024 Editor assigned by journal 29 Mar, 2024 First submitted to journal 28 Mar, 2024 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. 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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-4184317","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":288288171,"identity":"ba48419a-7c9f-4bf0-b714-6708bf8a5144","order_by":0,"name":"Hanwu Li","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Hanwu","middleName":"","lastName":"Li","suffix":""},{"id":288288172,"identity":"c2b27d48-a084-4ba0-ba76-d6d0e1584db0","order_by":1,"name":"Ning Ning","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYLCCBAYGOSiTmRj1zGAtxjykaQGCxB6itZiznz/24OGO2vT97KfTJBgqrBMbCGmx7ElmN0g8czy3hyd3mwTDmXTCWgwOJLNJJLYdy+1hAGphbDtMhJbzj8Fa0nn43wK1/CNGyw2wLTUJPBIgWxqI0GI547EZUMsBw54bbzdbJBxLNyaoxZw/8Znkz7Y6efb+3I03PtRYyxJ2GIQ6DKESCClH0lJHjNpRMApGwSgYqQAAKlE9V4ZkGWsAAAAASUVORK5CYII=","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":true,"prefix":"","firstName":"Ning","middleName":"","lastName":"Ning","suffix":""}],"badges":[],"createdAt":"2024-03-28 20:14:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4184317/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4184317/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40072-025-00354-3","type":"published","date":"2025-03-22T15:57:35+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":79120443,"identity":"7c5dff2b-a1be-493a-b5f4-24c802e242ec","added_by":"auto","created_at":"2025-03-24 16:08:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":484815,"visible":true,"origin":"","legend":"","description":"","filename":"submission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4184317/v1_covered_86bae3d3-a640-4f96-af07-f10558c77d8f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"stochastics-and-partial-differential-equations-analysis-and-computations","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"spde","sideBox":"Learn more about [Stochastics and Partial Differential Equations: Analysis and Computations](https://www.springer.com/journal/40072)","snPcode":"40072","submissionUrl":"https://submission.springernature.com/new-submission/40072/3","title":"Stochastics and Partial Differential Equations: Analysis and Computations","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"G-expectation, reflected backward SDE, nonlinear PDE, double obstacles MSC-classification: 60G65, 60H10, 60H30","lastPublishedDoi":"10.21203/rs.3.rs-4184317/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4184317/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). 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