{"paper":{"title":"Orlicz integrability of additive functionals of Harris ergodic Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rados{\\l}aw Adamczak, Witold Bednorz","submitted_at":"2012-01-17T17:33:48Z","abstract_excerpt":"For a Harris ergodic Markov chain $(X_n)_{n\\ge 0}$, on a general state space, started from the so called small measure or from the stationary distribution we provide optimal estimates for Orlicz norms of sums $\\sum_{i=0}^\\tau f(X_i)$, where $\\tau$ is the first regeneration time of the chain. The estimates are expressed in terms of other Orlicz norms of the function $f$ (wrt the stationary distribution) and the regeneration time $\\tau$ (wrt the small measure). We provide applications to tail estimates for additive functionals of the chain $(X_n)$ generated by unbounded functions as well as to c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3567","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":""},"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"}