{"paper":{"title":"Stochastic Currents of Fractional Brownian Motion: Existence and Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Herry Pribawanto Suryawan, Jose Luis da Silva, Martin Grothaus, Thomas Ullrich","submitted_at":"2024-08-20T15:19:53Z","abstract_excerpt":"By using white noise analysis, we study the integral kernel $\\xi(x)$, $x\\in\\mathbb{R}^{d}$, of stochastic currents corresponding to fractional Brownian motion with Hurst parameter $H\\in(0,1)$. For $x\\in\\mathbb{R}^{d}\\backslash\\{0\\}$ and $d\\ge1$ we show that the kernel $\\xi(x)$ is well-defined as a Hida distribution for all $H\\in(0,1)$. For $x=0$ and $d=1$, $\\xi(0)$ is a Hida distribution for all $H\\in(0,1)$. For $d\\ge2$, then $\\xi(0)$ is a Hida distribution only for $H\\in(0,1/d)$. For $d=1$, $x \\neq 0$, and $H \\in (0,1)$, we show that $\\xi(x) \\in \\mathcal{G}'$, the space of regular generalized"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10936","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.10936/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}