{"paper":{"title":"Regularizing properties of (non-Gaussian) transition semigroups in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"D. A. Bignamini, S. Ferrari","submitted_at":"2020-03-11T10:09:04Z","abstract_excerpt":"Let $\\mathcal{X}$ be a separable Hilbert space with norm $\\|\\cdot\\|$ and let $T>0$. 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 $W(t)$ 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}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.05195","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.05195/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"}