{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/analyzing-a-stochastic-process-driven-by","title":"Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise","arxiv_id":"1702.00032","date":"2017-01-31","proceeding":null,"authors":["B. Lehle","J. Peinke"],"abstract":"A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\\eta$ is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of $X$. Such a partially observed 2D-process could, e.g., be analyzed in a Bayesian framework using Markov chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamic of $X$ and its temporal derivative $\\dot X$ is analyzed. Subsequently the results can be used to determine the process parameters of $X$ and $\\eta$. In this paper, we propose a more direct approach that is purely based on the moments of the increments of $X$, which can be estimated for different time-increments $\\tau$ from a given time series. From a stochastic Taylor-expansion of $X$, analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.","url_abs":"http://arxiv.org/abs/1702.00032v1","url_pdf":"http://arxiv.org/pdf/1702.00032v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"analyzing-a-stochastic-process-driven-by","repo_url":"https://github.com/JonasRSV/DDPG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"analyzing-a-stochastic-process-driven-by","repo_url":"https://github.com/JonasRSV/PGTensorflow","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}