{"paper":{"title":"Temporal properties of the stochastic fractional heat equation with rough dependence in space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Beibei Zhang, Bin Qian","submitted_at":"2026-07-30T13:05:30Z","abstract_excerpt":"This paper investigates the nonlinear stochastic fractional heat equation driven by a Gaussian noise that is white in time and fractional in space with a Hurst parameter $H \\in \\big(\\frac{3-\\alpha}{4}, \\frac{1}{2}\\big)$. Specifically, the driving operator is the fractional Laplacian of order $\\alpha/2 \\in (1/2, 1)$. We characterize the asymptotic behavior of the temporal increment $u(t+\\varepsilon,x)-u(t,x)$ for fixed $t\\ge 0$ and $x\\in\\mathbb{R}$ as $\\varepsilon\\downarrow 0$. Utilizing these precise asymptotic estimates, we establish Khinchin's and Chung's laws of the iterated logarithm for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28167","kind":"arxiv","version":1},"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/2607.28167/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"}