{"paper":{"title":"Maximal $L^p$-regularity for stochastic evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Jan van Neerven, Lutz Weis, Mark Veraar","submitted_at":"2011-01-18T17:15:20Z","abstract_excerpt":"We prove maximal $L^p$-regularity for the stochastic evolution equation\n  \\[\\{{aligned} dU(t) + A U(t)\\, dt& = F(t,U(t))\\,dt + B(t,U(t))\\,dW_H(t), \\qquad t\\in [0,T],\n  U(0) & = u_0, {aligned}.\\] under the assumption that $A$ is a sectorial operator with a bounded $H^\\infty$-calculus of angle less than $\\frac12\\pi$ on a space $L^q(\\mathcal{O},\\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\\in (2,\\infty)$ and $q\\in [2,\\infty)$ and initial conditions $u_0$ in the real interpolation space $\\XAp $ we prove existence of unique strong solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3504","kind":"arxiv","version":4},"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"}