{"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/on-generating-fully-discrete-samples-of-the","title":"On generating fully discrete samples of the stochastic heat equation on an interval","arxiv_id":"2001.03403","date":"2020-01-10","proceeding":null,"authors":["Florian Hildebrandt"],"abstract":"Generalizing an idea of Davie and Gaines (2001), we present a method for the simulation of fully discrete samples of the solution to the stochastic heat equation on an interval. We provide a condition for the validity of the approximation, which holds particularly when the number of temporal and spatial observations tends to infinity. Hereby, the quality of the approximation is measured in total variation distance. In a simulation study we calculate temporal and spatial quadratic variations from sample paths generated both via our method and via naive truncation of the Fourier series representation of the process. Hereby, the results provided by our method are more accurate at a considerably lower computational cost.","url_abs":"http://arxiv.org/abs/2001.03403v1","url_pdf":"http://arxiv.org/pdf/2001.03403v1.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":"on-generating-fully-discrete-samples-of-the","repo_url":"https://github.com/pabolang/parabolicspdes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"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}