Composite Euler Method for Stochastic Differential Equations with Poisson Jumps

Composite Euler Method for Stochastic Differential Equations with Poisson Jumps | 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 Composite Euler Method for Stochastic Differential Equations with Poisson Jumps Yingpeng Duan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7153491/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 This paper proposes a new numerical method for stochastic differential equations with Poisson jumps (SDEJs), which is called the composite Euler method. This method draws on the strengths and avoids the weaknesses, effectively combining the advantages of the implicit Euler method and the explicit Euler method, and is superior to the single Euler method in terms of stability and convergence. At the end of the paper, numerical verification is carried out on the convergence and stability of the composite Euler method. MR(2020) Subject Classification 65H10; 65C30; 65L20 stochastic differential equations Poisson jumps Euler method Full Text Additional Declarations No competing interests reported. Supplementary Files manuscript.zip 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. 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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-7153491","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":489922022,"identity":"3abd7cb3-b1ea-4a7f-80f1-eeb20981ba9d","order_by":0,"name":"Yingpeng Duan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYBACfobDBww+8NjI2TczHyBOi2TjsYTCGTJpxgbsbQnEaTE4fEbhM4/N4UQDnjMGRLrs2BnGjTNy0hLMJXI+3njDYCen20BAB2PP2cMGH87Y5FnOyN1sOYch2djsAAEtzBLn0gxn9qQVM9zI3SbNw3AgcRshLWzyb8x/8/47nNhwI+cZcVp4GM4YGPPwHE7ccOYMG3FaJBiOJRjO4EkzlmxvM7acY0CEX+wPQKOSn5n54Y03FXZyBLWgWslDbNQgaSFVxygYBaNgFIwIAAB9dUlpOZMGbgAAAABJRU5ErkJggg==","orcid":"","institution":"Ganzhou Qiyuan Vocational College","correspondingAuthor":true,"prefix":"","firstName":"Yingpeng","middleName":"","lastName":"Duan","suffix":""}],"badges":[],"createdAt":"2025-07-18 03:38:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7153491/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7153491/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99310148,"identity":"3c110036-9866-4175-842c-a2ae7a46f8c8","added_by":"auto","created_at":"2025-12-31 16:12:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":360958,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7153491/v1_covered_a9110db8-a2d3-488a-ba1a-1e11af19a3b7.pdf"},{"id":87540870,"identity":"45d75739-f670-480d-bf16-fb702f3f7745","added_by":"auto","created_at":"2025-07-25 03:35:15","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":75994,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.zip","url":"https://assets-eu.researchsquare.com/files/rs-7153491/v1/98cdb90a1d645d0c2a0d6fd7.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Composite Euler Method for Stochastic Differential Equations with Poisson Jumps","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":"stochastic differential equations, Poisson jumps, Euler method","lastPublishedDoi":"10.21203/rs.3.rs-7153491/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7153491/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper proposes a new numerical method for stochastic differential equations with Poisson jumps (SDEJs), which is called the composite Euler method. 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