{"paper":{"title":"Limit value for optimal control with general means","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"J\\'er\\^ome Renault (GREMAQ), Marc Quincampoix (LM-Brest), Xiaoxi Li (IMJ-PRG)","submitted_at":"2015-03-17T22:42:15Z","abstract_excerpt":"We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\\`aro average. The limit of the value with Ces\\`aro mean when the horizon tends to infinity is widely studied in the literature. We address the more general question of the existence of a limit when the averaging parameter converges, for values defined with means of general types.\n  We consider a given function and a family of costs defined as the mean of the function with respect to a family of probability measures -- the evaluations -- on R_+. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05238","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"}