{"paper":{"title":"Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gersende Fort (LTCI)","submitted_at":"2013-09-12T11:27:24Z","abstract_excerpt":"This paper provides a Central Limit Theorem (CLT) for a process $\\{\\theta_n, n\\geq 0\\}$ satisfying a stochastic approximation (SA) equation of the form $\\theta_{n+1} = \\theta_n + \\gamma_{n+1} H(\\theta_n,X_{n+1})$; a CLT for the associated average sequence is also established. The originality of this paper is to address the case of controlled Markov chain dynamics $\\{X_n, n\\geq 0 \\}$ and the case of multiple targets. The framework also accomodates (randomly) truncated SA algorithms. Sufficient conditions for CLT's to hold are provided as well as comments on how these conditions extend previous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3116","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"}