{"paper":{"title":"Random Continued fractions: L\\'evy constant and Chernoff-type estimate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Bing Li, Lulu Fang, Min Wu, Narn-Rueih Shieh","submitted_at":"2016-01-10T12:13:36Z","abstract_excerpt":"Given a stochastic process $\\{A_n, n \\geq 1\\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1, A_2, \\cdots, A_n, \\cdots]$ analogue to the continued fraction expansion of real numbers. Assume that $\\{A_n, n \\geq 1\\}$ is ergodic and the expectation $E(\\log A_1) < \\infty$, we give a L\\'evy-type metric theorem which covers that of real case presented by L\\'evy in 1929. Moreover, a corresponding Chernoff-type estimate is obtained under the conditions $\\{A_n, n \\geq 1\\}$ is $\\psi$-mixing and for each $0< t< 1$, $E(A_1^t) < \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02205","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"}