Non-Markovianity of $2K-B$ and a degeneration

[2410.04051] Non-Markovianity of $2K-B$ and a degeneration Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2410.04051 (math) [Submitted on 5 Oct 2024 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Non-Markovianity of $2K-B$ and a degeneration Authors: Yang Chu , Lingfu Zhang View a PDF of the paper titled Non-Markovianity of $2K-B$ and a degeneration, by Yang Chu and 1 other authors View PDF HTML (experimental) Abstract: We study the process of $2K-B$, where $B$ is a standard one-dimensional Brownian motion and $K$ is its concave majorant. In light of Pitman's $2M-B$ theorem, it was recently conjectured by Ouaki and Pitman \cite{OP} that $2K-B$ has the law of the BES(5) process. The two processes share properties such as Brownian scaling, time inversion and quadratic variation, and the same one point distribution and infinitesimal generator, among many other evidences; and it remains to prove that $2K-B$ is Markovian. However, we show that this conjecture is false. To better understand the similarity between these two processes, we study a degeneration of $2K-B$. We show it is a mixture of BES(3), and get other properties including multiple points distribution, infinitesimal generator, and path decomposition at future infimum. We also further investigate the Markovian structure and the filtrations of $2K-B, B$ and $K$. Comments: 24 pages, 5 figures Subjects: Probability (math.PR) Cite as: arXiv:2410.04051 [math.PR] (or arXiv:2410.04051v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2410.04051 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Electronic Journal of Probability 30 (2025): 1-24 Related DOI : https://doi.org/10.1214/25-EJP1447 Focus to learn more DOI(s) linking to related resources Submission history From: Yang Chu [ view email ] [v1] Sat, 5 Oct 2024 06:10:16 UTC (1,449 KB) [v2] Tue, 14 Apr 2026 00:26:07 UTC (2,240 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-Markovianity of $2K-B$ and a degeneration, by Yang Chu and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2024-10 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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