{"paper":{"title":"Waiting times and stopping probabilities for patterns in Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dong Xu, Hui-Zeng Zhang, Min-Zhi Zhao","submitted_at":"2016-02-21T08:25:51Z","abstract_excerpt":"Suppose that $\\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\\mathcal C$ occurs as a run. This time is denoted by $\\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\\tau)$ and the stopping probabilities $P(\\tau=\\tau_A)$ with $A\\in\\mathcal C$, where $\\tau_A$ is the waiting time until the pattern $A$ appears as a run."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06512","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"}