{"paper":{"title":"Verifiable Conditions for the Irreducibility and Aperiodicity of Markov Chains by Analyzing Underlying Deterministic Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexandre Chotard, Anne Auger","submitted_at":"2015-08-07T09:52:27Z","abstract_excerpt":"We consider Markov chains that obey the following general non-linear state space model: $\\Phi_{k+1} = F(\\Phi_k, \\alpha(\\Phi_k, U_{k+1}))$ where the function $F$ is $C^1$ while $\\alpha$ is typically discontinuous and $\\{U_k: k \\in \\mathbb{Z}_{> 0} \\}$ is an independent and identically distributed process. We assume that for all $x$, the random variable $\\alpha(x, U_1)$ admits a density $p_x$ such that $(x, w) \\mapsto p_x(w)$ is lower semi-continuous.\n  We generalize and extend previous results that connect properties of the underlying deterministic control model to provide conditions for the ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01644","kind":"arxiv","version":4},"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"}