{"paper":{"title":"Moment bounds for a class of fractional stochastic heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"McSylvester Omaba, Mohammud Foondun, Wei Liu","submitted_at":"2014-09-19T15:04:26Z","abstract_excerpt":"We consider fractional stochastic heat equations of the form $\\frac{\\partial u_t(x)}{\\partial t} = -(-\\Delta)^{\\alpha/2} u_t(x)+\\lambda \\sigma (u_t(x)) \\dot F(t,\\, x)$. Here $\\dot F$ denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \\cite{CoKh}. Along the way, we prove a number of other interesting properties which extend and complement results in \\cite{foonjose}, \\cite{Khoshnevisan:2013aa} and \\cite{Khoshnevisan:2013ab}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5687","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"}