{"paper":{"title":"Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cheng-Der Fuh","submitted_at":"2004-07-08T14:41:23Z","abstract_excerpt":"Let {X_n,n\\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \\pi. Suppose an additive component\n S_n takes values in the real line R and is adjoined to the chain such that\n {(X_n,S_n),n\\geq0} is a Markov random walk. In this paper, we prove a uniform\n Markov renewal theorem with an estimate on the rate of convergence. This result is applied to boundary crossing problems for {(X_n,S_n),n\\geq0}.\n To be more precise, for given b\\geq0, define the stopping time \\tau=\\tau(b)=inf{n:S_n>b}.\n When a drift \\mu of the random walk S_n is 0, we deri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407140","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"}