{"paper":{"title":"Recurrence and transience property for a class of Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2012-03-02T12:51:03Z","abstract_excerpt":"We consider the recurrence and transience problem for a time-homogeneous Markov chain on the real line with transition kernel $p(x,\\mathrm{d}y)=f_x(y-x)\\,\\mathrm{d}y$, where the density functions $f_x(y)$, for large $|y|$, have a power-law decay with exponent $\\alpha(x)+1$, where $\\alpha(x)\\in(0,2)$. In this paper, under a uniformity condition on the density functions $f_x(y)$ and an additional mild drift condition, we prove that when $\\lim\\inf_{|x|\\longrightarrow\\infty}\\alpha(x)>1$, the chain is recurrent. Similarly, under the same uniformity condition on the density functions $f_x(y)$ and so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0447","kind":"arxiv","version":2},"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"}