Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets

[2603.07628] Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets Skip to main content Search Submit Donate Log in Mathematics > Probability arXiv:2603.07628 (math) [Submitted on 8 Mar 2026 ( v1 ), last revised 10 Mar 2026 (this version, v2)] Title: Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets Authors: Rachid Belfadli , Youssef Ouknine , Ercan Sönmez View PDF HTML (experimental) Abstract: In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fractional Brownian sheets with different Hurst parameters. Our analysis relies on techniques from two-parameter fractional calculus and a tailored version of Girsanov's theorem. The main challenge arises from the correlation between the two noises and the technical requirements for applying Girsanov's theorem in this setting. We show that, despite these difficulties, the additive noise regularizes the equation, allowing well-posedness under weak assumptions on the drift. Comments: 34 pages Subjects: Probability (math.PR) MSC classes: Primary 60H15, Secondary 60G22, 60H05 Cite as: arXiv:2603.07628 [math.PR] (or arXiv:2603.07628v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2603.07628 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Theoretical Probability (2026) Related DOI : https://doi.org/10.1007/s10959-026-01533-1 Focus to learn more DOI(s) linking to related resources Submission history From: Rachid Belfadli [ view email ] [v1] Sun, 8 Mar 2026 13:28:43 UTC (23 KB) [v2] Tue, 10 Mar 2026 07:54:53 UTC (23 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)

Related documents

• Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets#682605
• Hyperparameter Selection via Early Stopping for Bayesian Semilinear PDEs#984079
• Harmonic extension technique: probabilistic and analytic perspectives#1062755
• Sample Path Regularity of Non-autonomous Uniformly Parabolic Spdes#420261
• Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type#684327