{"paper":{"title":"On generators of transition semigroups associated to semilinear stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"D.A. Bignamini, S. Ferrari","submitted_at":"2020-10-08T11:36:39Z","abstract_excerpt":"Let $\\mathcal{X}$ be a real separable Hilbert space. Let $Q$ be a linear, self-adjoint, positive, trace class operator on $\\mathcal{X}$, let $F:\\mathcal{X}\\rightarrow\\mathcal{X}$ be a (smooth enough) function and let $\\{W(t)\\}_{t\\geq 0}$ be a $\\mathcal{X}$-valued cylindrical Wiener process. For $\\alpha\\in [0,1/2]$ we consider the operator $A:=-(1/2)Q^{2\\alpha-1}:Q^{1-2\\alpha}(\\mathcal{X})\\subseteq\\mathcal{X}\\rightarrow\\mathcal{X}$. We are interested in the mild solution $X(t,x)$ of the semilinear stochastic partial differential equation \\begin{gather} \\left\\{\\begin{array}{ll} dX(t,x)=\\big(AX(t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.03908","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.03908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}