{"paper":{"title":"Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Mohammud Foondun, Pejman Mahboubi","submitted_at":"2014-06-20T00:35:31Z","abstract_excerpt":"Consider the stochastic partial differential equation $\\partial_t u = Lu+\\sigma(u)\\xi$, where $\\xi$ denotes space-time white noise and $L:=-(-\\Delta)^{\\alpha/2}$ denotes the fractional Laplace operator of index $\\alpha/2\\in(\\nicefrac12\\,,1]$. We study the detailed behavior of the approximate spatial gradient $u_t(x)-u_t(x-\\varepsilon)$ at fixed times $t>0$, as $\\varepsilon\\downarrow0$. We discuss a few applications of this work to the study of the sample functions of the solution to the KPZ equation as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5246","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"}