[2404.09800] Fractional derivatives of local times for some Gaussian processes Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2404.09800 (math) [Submitted on 15 Apr 2024 ( v1 ), last revised 24 Apr 2026 (this version, v2)] Title: Fractional derivatives of local times for some Gaussian processes Authors: Minhao Hong , Qian Yu View a PDF of the paper titled Fractional derivatives of local times for some Gaussian processes, by Minhao Hong and 1 other authors View PDF HTML (experimental) Abstract: In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of the local time defined by Marchaud derivatives in $L^p(p\ge1)$ and show that these derivatives are Hölder continuous with respect to both time and space variables and are also continuous with respect to the order of derivatives. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time with the help of contour integration. Subjects: Probability (math.PR) Cite as: arXiv:2404.09800 [math.PR] (or arXiv:2404.09800v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2404.09800 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Minhao Hong [ view email ] [v1] Mon, 15 Apr 2024 13:57:13 UTC (21 KB) [v2] Fri, 24 Apr 2026 07:13:13 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Fractional derivatives of local times for some Gaussian processes, by Minhao Hong and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2024-04 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