{"paper":{"title":"Ladder epochs and ladder chain of a Markov random walk with discrete driving chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerold Alsmeyer","submitted_at":"2015-11-17T11:56:14Z","abstract_excerpt":"Let $(M_{n},S_{n})_{n\\ge 0}$ be a Markov random walk with positive recurrent driving chain $(M_{n})_{n\\ge 0}$ having countable state space $\\mathcal{S}$ and stationary distribution $\\pi$. It is shown in this note that, if the dual sequence $({}^{\\#}M_{n},{}^{\\#}S_{n})_{n\\ge 0}$ is positive divergent, i.e. ${}^{\\#}S_{n}\\to\\infty$ a.s., then the strictly ascending ladder epochs $\\sigma_{n}^{>}$ of $(M_{n},S_{n})_{n\\ge 0}$ are a.s. finite and the ladder chain $(M_{\\sigma_{n}^{>}})_{n\\ge 0}$ is positive recurrent on some $\\mathcal{S}^{>}\\subset\\mathcal{S}$. We also provide simple expressions for i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05361","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"}