{"paper":{"title":"Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dariusz Buraczewski, Ewa Damek, Mariusz Mirek","submitted_at":"2010-11-07T23:02:57Z","abstract_excerpt":"Let $\\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\\R^d$. We study the Markov chain $\\{X_n^x\\}_{n=0}^\\infty$ on $\\R^d$ defined by the recursion $X_n^x = \\Phi_n(X^x_{n-1})$, $n\\in\\N$, $X_0^x=x\\in\\R^d$. We assume that $\\Phi_n(x)=\\Phi(A_n x,B_n(x))$ for a fixed continuous function $\\Phi:\\R^d\\times \\R^d\\to\\R^d$, commuting with dilations and i.i.d random pairs $(A_n,B_n)$, where $A_n\\in {End}(\\R^d)$ and $B_n$ is a continuous mapping of $\\R^d$. Moreover, $B_n$ is $\\alpha$-regularly varying and $A_n$ has a faster decay at infinity than $B_n$. We prove that the stationary measure $\\nu$ of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1685","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"}