{"paper":{"title":"Deviation bounds for additive functionals of Markov process","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnaud Guillin (CEREMADE), Modal'x), Patrick Cattiaux (CMAP","submitted_at":"2006-03-01T12:57:03Z","abstract_excerpt":"In this paper we derive non asymptotic deviation bounds for $$\\P_\\nu (|\\frac 1t \\int_0^t V(X_s) ds - \\int V d\\mu | \\geq\n  R)$$ where $X$ is a $\\mu$ stationary and ergodic Markov process and $V$ is some $\\mu$ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\\mu$. Regularity means here that $\\mu$ may satisfy various functional inequalities (F-Sobolev, generalized Poincar\\'e etc...)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603021","kind":"arxiv","version":1},"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/math/0603021/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"}