{"paper":{"title":"The first returning speed and the last exit speed of a type of Markov chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huizeng Zhang, Lei Wang, Minzhi Zhao","submitted_at":"2011-01-06T08:19:55Z","abstract_excerpt":"Let $\\{X_n\\}$ be a Markov chain with transition probability $p_{ij}=a_{j-(i-1)^+},\\forall i,j\\ge 0$, where $a_j=0$ provided $j<0$, $a_0>0$, $a_0+a_1<1$ and $\\sum_{n=0}^\\infty a_n=1$. Let $\\mu=\\sum_{n=1}^\\infty na_n$. It's known that $\\{X_n\\}$ is positive recurrent when $\\mu<1$; is null recurrent when $\\mu=1$; and is transient when $\\mu>1$. In this paper, we shall discuss the first returning speed and the last exit speed more precisely by means of $\\{a_n\\}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1161","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"}