{"paper":{"title":"Nonconventional limit theorems in averaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Yuri Kifer","submitted_at":"2011-09-02T07:24:27Z","abstract_excerpt":"We consider \"nonconventional\" averaging setup in the form $\\frac {dX^\\epsilon(t)}{dt}=\\epsilon B\\big(X^\\epsilon(t),\\xi(q_1(t)), \\xi(q_2(t)),...,\\xi(q_\\ell(t))\\big)$ where $\\xi(t),t\\geq 0$ is either a stochastic process or a dynamical system (i.e. then $\\xi(t)=F^tx$) with sufficiently fast mixing while $q_j(t)=\\al_jt,\\,\\al_1<\\al_2<...<\\al_k$ and $q_j,\\, j=k+1,...,\\ell$ grow faster than linearly. We show that the properly normalized error term in the \"nonconventional\" averaging principle is asymptotically Gaussian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0373","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"}