{"paper":{"title":"Fluctuation theory for Markov random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabian Buckmann, Gerold Alsmeyer","submitted_at":"2016-08-30T09:16:09Z","abstract_excerpt":"Two fundamental theorems by Spitzer/Erickson and Kesten/Maller on the fluctuation type (positive divergence, negative divergence or oscillation) of a real-valued random walk $(S_{n})_{n\\ge 0}$ with iid increments $X_{1},X_{2},\\ldots$ and the existence of moments of various related quantities like the first passage into $[x,\\infty)$ and the last exit time from $(-\\infty,x]$ for arbitrary $x\\in\\mathbb{R}_{\\geqslant}$ are studied in the Markov-modulated situation when the $X_{n}$ are governed by a positive recurrent Markov chain $M=(M_{n})_{n\\ge 0}$ on a countable state space $\\mathcal{S}$, thus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08377","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"}