{"paper":{"title":"Improvements on the distribution of maximal segmental scores in a Markovian sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sabine Mercier, Simona Grusea","submitted_at":"2018-03-07T17:02:24Z","abstract_excerpt":"Let $(A_i)_{i \\geq 0}$ be a finite state irreducible aperiodic Markov chain and $f$ a lattice score function such that the average score is negative and positive scores are possible. Define $S_0:=0$ and $S_k:=\\sum_{i=1}^k f(A_i)$ the successive partial sums, $S^+$ the maximal non-negative partial sum, $Q_1$ the maximal segmental score of the first non-negative excursion and $M_n:=\\max_{0\\leq k\\leq\\ell\\leq n} (S_{\\ell}-S_k)$ the local score first defined by Karlin and Altschul (1990). We establish recursive formulae for the exact distribution of $S^+$ and derive new approximations for the distr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02769","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"}