A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs | 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 A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs Amir Haghighi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4023813/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 The main objective of this paper is to develop and analyze a numerical method for the strong approximation of solutions to highly nonlinear stiff It\^{o} stochastic differential equations (SDEs). In this method, we first divide the coefficients of the SDEs into linear and nonlinear parts. Then, in two fully explicit recursive phases, we apply the appropriate truncation transformation only to the nonlinear parts of the coefficients of the SDEs at each step. Theoretical aspects are introduced to establish the $L^q$-convergence theory of the new method in the finite time interval $[0,T]$. The stability and boundedness properties of the solutions generated by the new method are also investigated. An important contribution is that the region of MS-stability of the new method includes the region of MS-stability of the partially truncated method proposed by Yang et al. (2022). Moreover, we show that the proposed method preserves the exponential MS-stability and the asymptotic boundedness of the SDEs. Finally, numerical experiments are performed to compare the efficiency of this method with an existing explicit method developed for nonlinear SDEs. MSC Classification: 65C30 , 65L07 , 65L04 Stochastic differential equation locally Lipschitz SDEs truncated methods MS-stability asymptotic boundedness 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-4023813","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":277172361,"identity":"61a3de95-a9c1-4a87-92a9-ab4449c3444f","order_by":0,"name":"Amir Haghighi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIie2Rv2oCQRCHf8uCaeZiO2JyvsLIgQiCvsrJvUQqOQhcGl8gz2Gh6fbYwuYgraltLbwiwZArsuRPu6ddIPsxzS6/j52dAQKBPwkBKmeI1sad+OvOnKl00osUQEByXlvdPCrr1814ur6it+OpGaP7YJS98yhsrrP+bcXZ0320elwSg6sUZeV7xpD0ewVnYqMViN1fdkCZe4yBoeTjW6G9aoQxaFPE0KhXFzx1itaUutG1KUNLo4kqOBXbSfSNYRpW89yrxNtl8vJeLGbybPfq0CzieGtt7VOgXbnVzH9DP2tqQZ2AWWsqEAgE/i+fb5pIKoUhl8EAAAAASUVORK5CYII=","orcid":"","institution":"Razi University","correspondingAuthor":true,"prefix":"","firstName":"Amir","middleName":"","lastName":"Haghighi","suffix":""}],"badges":[],"createdAt":"2024-03-07 09:31:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4023813/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4023813/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53666942,"identity":"e9c003ef-37ed-4370-8f3a-9a780d1badfb","added_by":"auto","created_at":"2024-03-28 17:01:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":431265,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4023813/v1_covered_834c75c2-2220-4ee9-b866-5d89a170343c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs ","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 equation, locally Lipschitz SDEs, truncated methods, MS-stability, asymptotic boundedness","lastPublishedDoi":"10.21203/rs.3.rs-4023813/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4023813/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe main objective of this paper is to develop and analyze a numerical method for the strong approximation of solutions to highly nonlinear stiff It\\^{o} stochastic differential equations (SDEs). 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