{"paper":{"title":"On some random walk problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chak Hei Lo","submitted_at":"2018-02-19T13:38:12Z","abstract_excerpt":"In the first part of this thesis, we study a Markov chain on $\\mathbb{R}_+ \\times S$, where $\\mathbb{R}_+$ is the non-negative real numbers and $S$ is a finite set, in which when the $\\mathbb{R}_+$-coordinate is large, the $S$-coordinate of the process is approximately Markov with stationary distribution $\\pi_i$ on $S$. Denoting by $\\mu_i(x)$ the mean drift of the $\\mathbb{R}_+$-coordinate of the process at $(x,i) \\in \\mathbb{R}_+ \\times S$, we give an exhaustive recurrence classification in the case where $\\sum_{i} \\pi_i \\mu_i (x) \\to 0$, which is the critical regime for the recurrence-transi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06623","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"}