Multi-Dimensional Integral Fractional Ornstein-Uhlenbeck Process with Application on Animal Movement

Multi-Dimensional Integral Fractional Ornstein-Uhlenbeck Process with Application on Animal Movement | 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 Multi-Dimensional Integral Fractional Ornstein-Uhlenbeck Process with Application on Animal Movement Jose Hermenegildo Ramirez Gonzalez, Erick A. Chacón-Montalván, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7843642/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 Fractional Ornstein–Uhlenbeck (fOU) processes are essential for a wide range of applications because they can capture complex patterns, such as long-range dependence and memory effects, with the classical Ornstein–Uhlenbeck (OU) process as a special case. In this work, we extend the integral fractional Ornstein–Uhlenbeck (ifOU) process to the multidimensional case, focusing on its application to animal telemetry. Predicting animal trajectories is challenging due to intricate behaviors, unpredictable environmental factors, and limited precise movement data. We model multi-dimensional trajectories in terms of longitude, latitude, and altitude by representing the velocity of each dimension as a fOU process, with correlation induced by a multi-dimensional fractional Brownian motion. Consequently, the animal position is modeled by the resulting multi-dimensional integral fractional Ornstein–Uhlenbeck (mifOU) process. We propose efficient simulation, likelihood-based inference, and prediction algorithms. The applicability of our model to animal movement is demonstrated through simulation studies and the trajectory modeling of bats in Germany. Animal tracking Gaussian processes Long-range dependence Telemetry data 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. 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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-7843642","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":554421240,"identity":"8da8d65a-b501-4801-b3e2-ed2a8f97aa3d","order_by":0,"name":"Jose Hermenegildo Ramirez Gonzalez","email":"data:image/png;base64,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","orcid":"","institution":"King Abdullah University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Jose","middleName":"Hermenegildo Ramirez","lastName":"Gonzalez","suffix":""},{"id":554421242,"identity":"d45d78d3-c490-4d70-9450-9a424526788d","order_by":1,"name":"Erick A. 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