{"paper":{"title":"Moderate deviation principle for ergodic Markov chain. Lipschitz summands","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Juditsky, B. Delyon, R. Liptser","submitted_at":"2005-03-04T03:11:02Z","abstract_excerpt":"For ${1/2}<\\alpha<1$, we propose the MDP analysis for family $$ S^\\alpha_n=\\frac{1}{n^\\alpha}\\sum_{i=1}^nH(X_{i-1}), n\\ge 1, $$ where $(X_n)_{n\\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\\in \\mathbb{R}^d$, when the spectrum of operator $P_x$ is continuous. The vector-valued function $H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is required. The main helpful tools in our approach are Poisson's equation and Stochastic Exponential; the first enables to replace the original family by $\\frac{1}{n^\\alpha}M_n$ with a martingale $M_n$ while the second to avoid the direct "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503071","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"}