{"paper":{"title":"Asymptotic properties of some space-time fractional stochastic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mohammud Foondun","submitted_at":"2015-05-18T12:47:28Z","abstract_excerpt":"Consider non-linear time-fractional stochastic heat type equations of the following type, $$\\partial^\\beta_tu_t(x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\lambda \\sigma(u)\\stackrel{\\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$. The operator $\\partial^\\beta_t$ is the Caputo fractional derivative while $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process and $I^{1-\\beta}_t$ is the fractional integral operator. The forcing noise denoted by $\\stackrel{\\cdot}{F}(t,x)$ is a Gaussian noise. And the multiplicative non-linearity $\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04615","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"}