{"paper":{"title":"Limit theorems for stationary Markov processes with L2-spectral gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Deborah Ferre (IRMAR), James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","submitted_at":"2012-01-22T17:31:11Z","abstract_excerpt":"Let $(X_t, Y_t)_{t\\in T}$ be a discrete or continuous-time Markov process with state space $X \\times R^d$ where $X$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\\in T}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\\in T}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\\in T}$ is shown to satisfy the following cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4579","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"}