{"paper":{"title":"Temporal asymptotics for fractional parabolic Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Song, Xia Chen, Xiaoming Song, Yaozhong Hu","submitted_at":"2016-04-12T17:59:19Z","abstract_excerpt":"In this paper, we consider fractional parabolic equation of the form $ \\frac{\\partial u}{\\partial t}=-(-\\Delta)^{\\frac{\\alpha}{2}}u+u\\dot W(t,x)$, where $-(-\\Delta)^{\\frac{\\alpha}{2}}$ with $\\alpha\\in(0,2]$ is a fractional Laplacian and $\\dot W$ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by $\\alpha$-stable process. As a byproduct, we obtain the critical values for $\\theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03493","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"}