{"paper":{"title":"On lower limits and equivalences for distribution tails of randomly stopped sums","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Denisov, Dmitry Korshunov, Sergey Foss","submitted_at":"2007-01-31T13:00:00Z","abstract_excerpt":"For a distribution $F^{*\\tau}$ of a random sum $S_{\\tau}=\\xi_1+...+\\xi_{\\tau}$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0,\\infty)$, we study the limits of the ratios of tails $\\bar{F^{*\\tau}}(x)/\\bar{F}(x)$ as $x\\to\\infty$ (here, $\\tau$ is a counting random variable which does not depend on $\\{\\xi_n\\}_{n\\ge1}$). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701920","kind":"arxiv","version":3},"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"}