{"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/spiking-and-collapsing-in-large-noise-limits","title":"Spiking and collapsing in large noise limits of SDEs","arxiv_id":"1810.05629","date":"2018-10-12","proceeding":null,"authors":["Cédric Bernardin","Raphaël Chetrite","Reda Chhaibi","Joseph Najnudel","Clément Pellegrini"],"abstract":"We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an intriguing behavior. As the noise grows larger, the solutions exhibit locally a collapsing, that is to say, converge to pure jump processes very reminiscent of a metastability phenomenon. But surprisingly the limiting jump process is decorated by a spike process. We give a precise meaning to the convergence and completely prove these statements for a large class of one-dimensional diffusions, thanks to a robust strategy of proof.","url_abs":"https://arxiv.org/abs/1810.05629v3","url_pdf":"https://arxiv.org/pdf/1810.05629v3.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":"spiking-and-collapsing-in-large-noise-limits","repo_url":"https://github.com/redachhaibi/quantumcollapse","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}