{"paper":{"title":"Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fei Pu, Robert C. Dalang","submitted_at":"2018-10-12T07:36:51Z","abstract_excerpt":"We consider a system of $d$ non-linear stochastic fractional heat equations in spatial dimension $1$ driven by multiplicative $d$-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of $(u(s, y), u (t, x))$. From this result, we deduce optimal lower bounds on hitting probabilities of the process $\\{u(t, x): (t, x) \\in [0, \\infty[ \\times \\mathbb{R}\\}$ in the non-Gaussian case, in terms of Newtonian capacity, which is as sharp as that in the Gaussian case. This also improves the result in Dalang, Khoshnevisan and Nualar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05386","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"}