{"paper":{"title":"Asymptotics of randomly stopped sums in the presence of heavy tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Denisov, Dmitry Korshunov, Sergey Foss","submitted_at":"2008-08-27T13:04:56Z","abstract_excerpt":"We study conditions under which $P(S_\\tau>x)\\sim P(M_\\tau>x)\\sim E\\tau P(\\xi_1>x)$ as $x\\to\\infty$, where $S_\\tau$ is a sum $\\xi_1+...+\\xi_\\tau$ of random size $\\tau$ and $M_\\tau$ is a maximum of partial sums $M_\\tau=\\max_{n\\le\\tau}S_n$. Here $\\xi_n$, $n=1$, 2, ..., are independent identically distributed random variables whose common distribution is assumed to be subexponential. We consider mostly the case where $\\tau$ is independent of the summands; also, in a particular situation, we deal with a stopping time.\n  Also we consider the case where $E\\xi>0$ and where the tail of $\\tau$ is compar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3697","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"}