Persistence Probability of Fractional Brownian Motion with Random Hurst Exponent

[2603.14934] Persistence Probability of Fractional Brownian Motion with Random Hurst Exponent Skip to main content Search Submit Donate Log in Mathematics > Probability arXiv:2603.14934 (math) [Submitted on 16 Mar 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Persistence Probability of Fractional Brownian Motion with Random Hurst Exponent Authors: Frank Aurzada , Sabine Müller View PDF HTML (experimental) Abstract: We study the persistence properties of a fractional Brownian motion whose Hurst exponent is a random variable instead of a fixed constant. For each fixed $H \in (0,1)$, it is well known that the persistence probability of an FBM below a constant barrier decays like $T^{-(1-H)+o(1)}$, as $T$ tends to infinity, cf. Molchan (1999). Our object of interest is the persistence probability of the process resulting from first randomly selecting $H\in (0,1)$ and then considering a fractional Brownian motion with this value of $H$ as a Hurst exponent, a process that is referred to as a fractional Brownian motion with random exponent. We prove that its persistence probability decays as $T^{-(1-H_0)+o(1)}$, as $T$ tends to infinity, where $H_0$ is the essential supremum of the distribution of the random Hurst exponent. Comments: Technical correction to Corollary 4.2, with corresponding changes in Proposition 4.6 and the proof of the upper bound. The main results are unaffected Subjects: Probability (math.PR) Cite as: arXiv:2603.14934 [math.PR] (or arXiv:2603.14934v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2603.14934 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Phys. A: Math. Theor. 59 (2026) 255001 Related DOI : https://doi.org/10.1088/1751-8121/ae7aca Focus to learn more DOI(s) linking to related resources Submission history From: Sabine Müller [ view email ] [v1] Mon, 16 Mar 2026 07:37:05 UTC (66 KB) [v2] Fri, 28 Aug 2026 06:52:22 UTC (63 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-03 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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