{"paper":{"title":"Weak Moment of a Class of Stochastic Heat Equation with Martingale-valued Harmonic Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ejighikeme McSylvester Omaba","submitted_at":"2017-06-07T22:33:12Z","abstract_excerpt":"A study of a non-linear parabolic SPDEs of the form $\\partial_{t}u=\\mathcal{L}\\,u + \\sigma(u)f(B_t^x,t)\\dot{w}$ with $\\dot{w}$ as the space-time white noise and $f(B_t^x,t)$ a space-time harmonic function was done. The function $\\sigma:\\mathbb{R}\\rightarrow\\mathbb{R}$ is Lipschitz continuous and $\\mathcal{L}$ the $L^2$-generator of a L\\'{e}vy process. Some precise condition for existence and uniqueness of the solution were given and we show that the solution grows weakly(in law/distribution) in time (for large $t$) at most a precise exponential rate for the $\\mathcal{L}$; and grows in time at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02402","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"}