{"paper":{"title":"Asymptotic self-similarity and order-two ergodic theorems for renewal flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Albert M. Fisher, Marina Talet","submitted_at":"2013-04-03T00:35:51Z","abstract_excerpt":"We prove a log average almost-sure invariance principle (log asip) for renewal processes with positive i.i.d. gaps in the domain of attraction of an $\\alpha$-stable law with $0<\\alpha<1$. Dynamically, this means that renewal and Mittag-Leffler paths are forward asymptotic in the scaling flow, up to a time average. This strengthens the almost-sure invariance principle in log density we proved in {FisherTalet2011}. The scaling flow is a Bernoulli flow on a probability space. We study a second flow, the increment flow, transverse to the scaling flow, which preserves an infinite invariant measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0816","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"}