{"paper":{"title":"Iterated random functions and regularly varying tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ewa Damek, Piotr Dyszewski","submitted_at":"2017-06-13T00:47:26Z","abstract_excerpt":"We consider solutions to so-called stochastic fixed point equation $R \\stackrel{d}{=} \\Psi(R)$, where $\\Psi $ is a random Lipschitz function and $R$ is a random variable independent of $\\Psi$. Under the assumption that $\\Psi$ can be approximated by the function $x \\mapsto Ax+B$ we show that the tail of $R$ is comparable with the one of $A$, provided that the distribution of $\\log (A\\vee 1) $ is tail equivalent. In particular we obtain new results for the random difference equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03876","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"}