{"paper":{"title":"Khinchin's and Chung's Laws of the Iterated Logarithm at Time Zero for the Linear Stochastic Fractional Diffusion Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chang Liu, Ran Wang","submitted_at":"2026-08-05T10:05:15Z","abstract_excerpt":"We consider the linear stochastic fractional diffusion equation \\begin{equation*} \\partial^{\\beta} u(t,x)=-\\left(-\\Delta\\right)^{\\alpha/2}u(t,x) +I_t^{\\gamma}\\bigl[\\dot W(t,x)\\bigr], \\qquad t>0,\\quad x\\in\\mathbb R^d, \\end{equation*} with zero initial conditions, where $\\alpha>0$, $\\beta\\in(0,2)$, and $\\gamma\\ge0$. The driving noise $\\dot W$ is a centered Gaussian generalized field that is fractional in time and has Riesz-type spatial covariance. For each fixed $x\\in\\mathbb R^d$, we establish a Khinchin-type law of the iterated logarithm at time zero for the temporal process $t\\mapsto u(t,x)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04644","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/2608.04644/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"}