{"paper":{"title":"Sharp Space-Time Regularity of the Solution to Stochastic Heat Equation Driven by Fractional-Colored Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dongsheng Wu, Randall Herrell, Renming Song, Yimin Xiao","submitted_at":"2018-09-28T19:57:24Z","abstract_excerpt":"In this paper, we study the following stochastic heat equation \\[\n  \\partial_tu=\\mathcal{L} u(t,x)+\\dot{B},\\quad\n  u(0,x)=0,\\quad 0\\le t\\le T,\\quad x\\in\\mathbb{R}d, \\] where $\\mathcal{L}$ is the generator of a L\\'evy process $X$ taking value in $\\mathbb{R}^d$, $B$ is a fractional-colored Gaussian noise with Hurst index $H\\in\\left(\\frac12,\\,1\\right)$ for the time variable and spatial covariance function $f$ which is the Fourier transform of a tempered measure $\\mu.$\n  After establishing the existence of solution for the stochastic heat equation, we study the regularity of the solution $\\{u(t,x)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00066","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":""},"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"}