{"paper":{"title":"Large deviation estimates for exceedance times of perpetuity sequences and their dual processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dariusz Buraczewski, Ewa Damek, Jacek Zienkiewicz, Jeffrey F. Collamore","submitted_at":"2014-11-27T20:18:07Z","abstract_excerpt":"In a variety of problems in pure and applied probability, it is of relevant to study the large exceedance probabilities of the perpetuity sequence $Y_n := B_1 + A_1 B_2 + \\cdots + (A_1 \\cdots A_{n-1}) B_n$, where $(A_i,B_i) \\subset (0,\\infty) \\times {\\mathbb R}$. Estimates for the stationary tail distribution of $\\{ Y_n \\}$ have been developed in the seminal papers of Kesten (1973) and Goldie (1991). Specifically, it is well-known that if $M := \\sup_n Y_n$, then ${\\mathbb P} \\left\\{ M > u \\right\\} \\sim {\\cal C}_M u^{-\\xi}$ as $u \\to \\infty$. While much attention has been focused on extending t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7693","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"}