{"paper":{"title":"Explicit contraction rates for a class of degenerate and infinite-dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raphael Zimmer","submitted_at":"2016-05-25T12:56:26Z","abstract_excerpt":"Given a separable and real Hilbert space $\\mathbb{H}$ and a trace-class, symmetric and non-negative operator $\\mathcal{G}:\\mathbb{H}\\rightarrow\\mathbb{H}$, we examine the equation \\begin{align*}\n  dX_t = -X_t\\, dt + b(X_t) \\, dt + \\sqrt{2} \\, dW_t, \\qquad X_0=x\\in\\mathbb{H},\n  \\end{align*} where $(W_t)$ is a $\\mathcal{G}$-Wiener process on $\\mathbb{H}$ and $b:\\mathbb{H}\\rightarrow\\mathbb{H}$ is Lipschitz. We assume there is a splitting of $\\mathbb{H}$ into a finite-dimensional space $\\mathbb{H}^l$ and its orthogonal complement $\\mathbb{H}^h$ such that $\\mathcal{G}$ is strictly positive definit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07863","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":""},"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"}