{"paper":{"title":"Ergodic Theory for Controlled Markov Chains with Stationary Inputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.AP"],"primary_cat":"cs.PF","authors_text":"Ana Bu\\v{s}i\\'c, Sean Meyn, Yue Chen","submitted_at":"2016-04-14T02:16:52Z","abstract_excerpt":"Consider a stochastic process $\\{X(t)\\}$ on a finite state space $ {\\sf X}=\\{1,\\dots, d\\}$. It is conditionally Markov, given a real-valued `input process' $\\{\\zeta(t)\\}$. This is assumed to be small, which is modeled through the scaling, \\[ \\zeta_t = \\varepsilon \\zeta^1_t, \\qquad 0\\le \\varepsilon \\le 1\\,, \\] where $\\{\\zeta^1(t)\\}$ is a bounded stationary process. The following conclusions are obtained, subject to smoothness assumptions on the controlled transition matrix and a mixing condition on $\\{\\zeta(t)\\}$:\n  (i) A stationary version of the process is constructed, that is coupled with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04013","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"}