{"paper":{"title":"A strong averaging principle for L\\'evy diffusions in foliated spaces with unbounded leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michael A. H\\\"ogele, Paulo-Henrique da Costa, Paulo R. Ruffino","submitted_at":"2018-02-02T16:53:38Z","abstract_excerpt":"This article extends a strong averaging principle for L\\'evy diffusions which live on the leaves of a foliated manifold subject to small transversal L\\'evy type perturbation to the case of non-compact leaves. The main result states that the existence of $p$-th moments of the foliated L\\'evy diffusion for $p\\geq 2$ and an ergodic convergence of its coefficients in $L^p$ implies the strong $L^p$ convergence of the fast perturbed motion on the time scale $t/\\epsilon$ to the system driven by the averaged coefficients. In order to compensate the non-compactness of the leaves we use an estimate of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01456","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"}