{"paper":{"title":"Paul L\\'evy, strong approximation and the St. Petersburg paradox","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Istv\\'an Berkes","submitted_at":"2016-09-27T08:57:13Z","abstract_excerpt":"This paper discusses a forgotten remark of Paul L\\'evy (1935), determining the asymptotic distribution of sums of i.i.d. random variables with tails $cx^{-\\alpha}\\psi(\\log x)$, where $0<\\alpha<2$ and $\\psi$ is a periodic function on $\\mathbb R$. Such sums occur in the St. Petersburg paradox and L\\'evy's results precede the crucial results of Martin-L\\\"of (1985) and Cs\\\"org\\H{o} and Dodunekova (1991) on the paradox by 50 years. L\\'evy's proof uses a coupling argument similar to Skorohod representation and provides a strong (pointwise) approximation result, the first in probability theory. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08321","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"}