Correction terms for parametric white noise processes. Gaussian, Poissonian and α-stable

Correction terms for parametric white noise processes. Gaussian, Poissonian and α-stable | 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 Correction terms for parametric white noise processes. Gaussian, Poissonian and α-stable Rossella Laudani, Mario Di Paola, Giovanni Falsone This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6862218/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 work, the important rules of the stochastic differential calculus, when the external and parametric (or multiplicative) excitations are modeled as Gaussian white noise processes, are generalized to the case of non-Gaussian white noise excitations. This extension began some years ago, when the classical Gaussian stochastic differential calculus was generalized to thePoisson delta-correlated actions. In the present work, the extension has been completed considering the more general class of white noise excitations, which are α-stable Lévy white noises. It is shown that, in the case of parametric excitations, this extension also regards the correction terms necessary for using the Ito-type integration. These results have been possible thanks to the evidence that all the white processes here considered belong to a class of processes (the motion ones), whose formal derivative is just an element of the white noise class. Stochastic differential calculus parametric α-stable processes Itˆo calculus correction terms 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. 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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-6862218","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":472809565,"identity":"b88a8672-de81-44a5-ab31-7d7e4bf09bde","order_by":0,"name":"Rossella Laudani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYDACdiDmASJ+IH0AwiYEmKFaJBugWgjrgWphMDgAFSCoxbyZ+ZnEm5o7MsY3cg8eulHBIGNPSIvMYTYzyTnHnvGY3chLOJxzhgiHSTAzmEnzsB0GaskxOJzbRpQW9m/SPP8O8xjPAGn5R5QWHjNp3rbDPAYSIC0NxGkptpzbd5hH4swbg8M5xyR4eA4Q0sLevvHGm2+H7fnbc4w/59TY2LM3ELIG3QgS1Y+CUTAKRsEowAoAm6U0vQVPJ/sAAAAASUVORK5CYII=","orcid":"","institution":"University of Messina","correspondingAuthor":true,"prefix":"","firstName":"Rossella","middleName":"","lastName":"Laudani","suffix":""},{"id":472809566,"identity":"dc9f9056-2d03-4864-9717-e1dcdb7cb650","order_by":1,"name":"Mario Di Paola","email":"","orcid":"","institution":"University of Palermo","correspondingAuthor":false,"prefix":"","firstName":"Mario","middleName":"Di","lastName":"Paola","suffix":""},{"id":472809567,"identity":"7e780db7-ad6b-4fed-9009-54847381a25d","order_by":2,"name":"Giovanni Falsone","email":"","orcid":"","institution":"University of Messina","correspondingAuthor":false,"prefix":"","firstName":"Giovanni","middleName":"","lastName":"Falsone","suffix":""}],"badges":[],"createdAt":"2025-06-10 10:53:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6862218/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6862218/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87159593,"identity":"5204ea07-db46-42d2-bc62-df79be32e423","added_by":"auto","created_at":"2025-07-21 04:17:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2386863,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6862218/v1_covered_c5e6a664-b0c6-4cb7-8990-373fd22c3935.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Correction terms for parametric white noise processes. 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