Generalized Wright Analysis: Stochastic and Applications

Generalized Wright Analysis: Stochastic and Applications | 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 Generalized Wright Analysis: Stochastic and Applications Wolfgang Bock, Lorenzo Cristofaro, Joses L. da Silva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8128059/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract In this paper, we investigate the stochastic counterpart of the generalized Wright analysis introduced in Beghin et al.~ in Integral Equations and Operator Theory, 97, 2025. We define a new class of non-Gaussian and non-Markovian processes, called the generalized Fox-H process, which extends well-known processes such as fractional Brownian motion and generalized grey Brownian motion. We study their joint probability density and covariance, showing the stationarity of their increments. In addition, this process has H{\"o}lder continuous paths and is represented as a time-change of fractional Brownian motion. We characterize the generalized Fox-$H$ noise as an element in the distribution space $(\mathcal{S})^{-1}_{\mu_\Psi}$. We conclude by establishing the existence of local times and discussing their anomalous diffusion properties. MSC Classification: 33E12 , 60E05 , 60G18 , 60G20 , 60G22 Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 30 Mar, 2026 Reviews received at journal 25 Mar, 2026 Reviews received at journal 15 Jan, 2026 Reviewers agreed at journal 25 Nov, 2025 Reviewers agreed at journal 24 Nov, 2025 Reviewers invited by journal 24 Nov, 2025 Editor assigned by journal 23 Nov, 2025 Submission checks completed at journal 17 Nov, 2025 First submitted to journal 16 Nov, 2025 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-8128059","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":550735451,"identity":"a0ad8414-0cf9-4e56-a973-8c78a0a8b9d8","order_by":0,"name":"Wolfgang Bock","email":"","orcid":"","institution":"Linnaeus University","correspondingAuthor":false,"prefix":"","firstName":"Wolfgang","middleName":"","lastName":"Bock","suffix":""},{"id":550735452,"identity":"b4c676ab-6968-4b4f-ab7a-2da85796690e","order_by":1,"name":"Lorenzo Cristofaro","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIie3RMUsDMRTA8RcOLsujtz45qV/hyQ0OVvwqLcJNCjfeWDiIS7sH9HN0TinUJfoFnErB+aDg4g3mKiJFEh075A8Jj0d+UwBisSNs8DOKqbuG7iQGgOHUR9IDYqDod+Oe4D+I64sg97OfyPlmW3UjyB5Wza6t+ezifvaeV5WDxkPwqSg0lkAvE0XG8vmjfV7kmgOEyjRHWgGjULBUndB0t8gxTOQH8p407VLxtabbt79ImuB4T6bkyMSRNExwneRoSiQrFFnLNxrXxSUy4YmHZFKJHXajYTaT27au+UrLZvPabwYe8t2vX6Dw+1gsFosF+wRgEUmWkZtudAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Luxembourg","correspondingAuthor":true,"prefix":"","firstName":"Lorenzo","middleName":"","lastName":"Cristofaro","suffix":""},{"id":550735453,"identity":"065706c9-ac9d-4a02-aedf-c11e14c0b3bd","order_by":2,"name":"Joses L. da Silva","email":"","orcid":"","institution":"Universidade da Madeira","correspondingAuthor":false,"prefix":"","firstName":"Joses","middleName":"L. da","lastName":"Silva","suffix":""}],"badges":[],"createdAt":"2025-11-16 15:08:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8128059/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8128059/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96959025,"identity":"0edef83a-f0a9-4569-8d62-31ee30a2a1ca","added_by":"auto","created_at":"2025-11-28 04:25:30","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4081,"visible":true,"origin":"","legend":"","description":"","filename":"0b906a7b97e64b729628c1fc79cfa8d6.json","url":"https://assets-eu.researchsquare.com/files/rs-8128059/v1/00b696ed067fb84bbdef02eb.json"},{"id":96959026,"identity":"f2c66ba6-177b-435e-a902-da7825d88010","added_by":"auto","created_at":"2025-11-28 04:25:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":398073,"visible":true,"origin":"","legend":"","description":"","filename":"GeneralizedWrightAnalysisStochasticandApplications.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8128059/v1_covered_26a565d7-2bab-4195-8c42-1e8925c019b4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Generalized Wright Analysis: Stochastic and Applications","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-theoretical-probability","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jotp","sideBox":"Learn more about [Journal of Theoretical Probability](http://link.springer.com/journal/10959)","snPcode":"10959","submissionUrl":"https://submission.nature.com/new-submission/10959/3","title":"Journal of Theoretical Probability","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8128059/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8128059/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we investigate the stochastic counterpart of the generalized Wright analysis introduced in Beghin et al.~ in Integral Equations and Operator Theory, \u0026nbsp;97, 2025. 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