{"paper":{"title":"Precise Tail Asymptotics for Attracting Fixed Points of Multivariate Smoothing Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dariusz Buraczewski, Sebastian Mentemeier","submitted_at":"2015-02-09T08:47:50Z","abstract_excerpt":"Given $d \\ge 1$, let $(A_i)_{i\\ge 1}$ be a sequence of random $d\\times d$ real matrices and $Q$ be a random vector in $\\mathbb{R}^d$. We consider fixed points of multivariate smoothing transforms, i.e. random variables $X\\in \\mathbb{R}^d$ satisfying $X$ has the same law as $\\sum_{i \\ge 1} A_i X_i + Q$, where $(X_i)_{i \\ge 1}$ are i.i.d. copies of $X$ and independent of $(Q, (A_i)_{i \\ge 1})$. The existence of fixed points that can attract point masses can be shown by means of contraction arguments. Let $X$ be such a fixed point. Assuming that the action of the matrices is expanding as well wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02397","kind":"arxiv","version":2},"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"}