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- Title
Tail-homogeneity of stationary measures for some multidimensional stochastic recursions.
- Authors
Buraczewski, Dariusz; Damek, Ewa; Guivarc'h, Yves; Hulanicki, Andrzej; Urban, Roman
- Abstract
We consider a stochastic recursion X n+1 = M n+1 X n + Q n+1, ( $${n\in \mathbb {N}}$$), where ( Q n, M n) are i.i.d. random variables such that Q n are translations, M n are similarities of the Euclidean space $${\mathbb {R}^d}$$ and $${X_n\in \mathbb {R}^d}$$. In the present paper we show that if the recursion has a unique stationary measure ν with unbounded support then the weak limit of properly dilated ν exists and defines a homogeneous tail measure Λ. The structure of Λ is studied and the supports of ν and Λ are compared. In particular, we obtain a product formula for Λ.
- Subjects
STOCHASTIC analysis; MATRIX analytic methods; INTEGRAL theorems; HOMOMORPHISMS; BOREL subgroups; RADON measures
- Publication
Probability Theory & Related Fields, 2009, Vol 145, Issue 3/4, p385
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-008-0172-8