{"paper":{"title":"Stationary and Transition Probabilities in Slow Mixing, Long Memory Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Meysam Asadi, Narayana P. Santhanam, Ramezan Paravi Torghabeh","submitted_at":"2013-01-28T22:16:36Z","abstract_excerpt":"We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\\emph{model}) over a finite alphabet $\\mathcal{A}$. Given any string $\\bf{w}$ of symbols from $\\mathcal{A}$ we want estimates of the conditional probability distribution of symbols following $\\bf{w}$, as well as the stationary probability of $\\bf{w}$. Two distinct problems that complicate estimation in this setting are (i) long memory, and (ii) \\emph{slow mixing} which could happen even with only one bit of memory.\n  Any consistent estimator in this setting can only converge pointwise over the class of al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6798","kind":"arxiv","version":17},"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"}