{"paper":{"title":"Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andr\\'e S\\\"u\\ss, Marta Sanz-Sol\\'e","submitted_at":"2013-12-04T17:40:48Z","abstract_excerpt":"We consider the family of stochastic partial differential equations indexed by a parameter $\\eps\\in(0,1]$, \\begin{equation*} Lu^{\\eps}(t,x) = \\eps\\sigma(u^\\eps(t,x))\\dot{F}(t,x)+b(u^\\eps(t,x)), \\end{equation*} $(t,x)\\in(0,T]\\times\\Rd$ with suitable initial conditions. In this equation, $L$ is a second-order partial differential operator with constant coefficients, $\\sigma$ and $b$ are smooth functions and $\\dot{F}$ is a Gaussian noise, white in time and with a stationary correlation in space. Let $p^\\eps_{t,x}$ denote the density of the law of $u^\\eps(t,x)$ at a fixed point $(t,x)\\in(0,T]\\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1257","kind":"arxiv","version":2},"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"}