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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.1685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"98d1bb6b70ccd4c13f7b64c50835680d238eb36307ebddf5075abf1d0c4ef981","abstract_canon_sha256":"126e615433265271443d62a9cd86b5fb3d3b798b979a21ed4041f36d5c6ce700"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:47.144338Z","signature_b64":"APtAi1rHYgwHUQ5mS8+91pIOnUtsbyGi8kHdTmTz6+Ep1vA5agVUkUB9rmVtIiW21MdF3ctzD7lkHBnkx//qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","last_reissued_at":"2026-05-18T04:10:47.143856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:47.143856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $B_n$. 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