{"paper":{"title":"General limit value in Dynamic Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"J\\'er\\^ome Renault (GREMAQ)","submitted_at":"2013-01-03T13:24:04Z","abstract_excerpt":"We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the \"patience\" of the decision-maker tends to infinity ? We consider, for each evaluation $\\theta$ (a probability distribution over positive integers) the value function $v_{\\theta}$ of the problem where the weight of any stage $t$ is given by $\\theta_t$, and we investigate the uniform convergence of a sequence $(v_{\\theta^k})_k$ when the \"impatience\" of the evaluations vanishes, in the sense that $\\sum_{t} |\\theta^k_{t}-\\theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0451","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"}