Modeling Stochastic Processes with Trees

Modeling Stochastic Processes with Trees | 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Share Download PDF Research Article Modeling Stochastic Processes with Trees Kartik Tyagi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8239083/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 In this paper, we show a deep connection between a new method to create randomly generated trees and stochastic calculus. Using computer simulations to generate matrices we are able to relate their height and width to the drift and diffusion of the classic stochastic differential equation. This approach lets us relate randomization to geometry, and simplify numerical approaches for differential equations containing stochastic variables. Applied Mathematics Computational Mathematics Stochastic processes Branching processes Brownian motion Diffusion approximation Invariance principle Stochastic differential equations Geometric probability Random trees Full Text Additional Declarations The authors declare no competing interests. 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-8239083","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":552762852,"identity":"bdf77bb7-b855-4af7-b9fb-d483c03ba4cf","order_by":0,"name":"Kartik Tyagi","email":"data:image/png;base64,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","orcid":"","institution":"Montgomery County Community College","correspondingAuthor":true,"prefix":"","firstName":"Kartik","middleName":"","lastName":"Tyagi","suffix":""}],"badges":[],"createdAt":"2025-11-29 20:25:35","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8239083/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8239083/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97249846,"identity":"a1624a23-105b-4373-be35-ebd68d0a67a4","added_by":"auto","created_at":"2025-12-02 13:13:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":483031,"visible":true,"origin":"","legend":"","description":"","filename":"ModelingStochasticProcesseswithTrees.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8239083/v1_covered_6bdbab87-37f9-4226-82dc-5fb8aec6f11c.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eModeling Stochastic Processes with Trees\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Montgomery County Community College","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 processes, Branching processes, Brownian motion, Diffusion approximation, Invariance principle, Stochastic differential equations, Geometric probability, Random trees","lastPublishedDoi":"10.21203/rs.3.rs-8239083/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8239083/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we show a deep connection between a new method to create randomly generated trees and stochastic calculus. 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