{"paper":{"title":"Importance sampling of heavy-tailed iterated random functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bert Zwart, Bohan Chen, Chang-han Rhee","submitted_at":"2016-09-11T16:53:52Z","abstract_excerpt":"We consider a stochastic recurrence equation of the form $Z_{n+1} = A_{n+1} Z_n+B_{n+1}$, where $\\mathbb{E}[\\log A_1]<0$, $\\mathbb{E}[\\log^+ B_1]<\\infty$ and $\\{(A_n,B_n)\\}_{n\\in\\mathbb{N}}$ is an i.i.d. sequence of positive random vectors. The stationary distribution of this Markov chain can be represented as the distribution of the random variable $Z \\triangleq \\sum_{n=0}^\\infty B_{n+1}\\prod_{k=1}^nA_k$. Such random variables can be found in the analysis of probabilistic algorithms or financial mathematics, where $Z$ would be called a stochastic perpetuity. If one interprets $-\\log A_n$ as t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03182","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"}