{"paper":{"title":"Quasi-compactness of Markov kernels on weighted-supremum spaces and geometrical ergodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Guibourg (IRMAR), James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","submitted_at":"2011-10-14T15:13:13Z","abstract_excerpt":"Let $P$ be a Markov kernel on a measurable space $\\X$ and let $V:\\X\\r[1,+\\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\\cB_V,\\|\\cdot\\|_V)$ of all the measurable functions $f : \\X\\r\\C$ such that $\\|f\\|_V := \\sup_{x\\in \\X} |f(x)|/V(x) < \\infty$. Furthermore we give bounds for the essential spectral radius of $P$. Under additional assumptions, these results allow us to derive the convergence rate of $P$ on $\\cB_V$, that is the geometric rate of convergence of the iterates $P^n$ to the stationary distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3240","kind":"arxiv","version":5},"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"}