Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

@article{Buraczewski2008TailhomogeneityOS,
  title={Tail-homogeneity of stationary measures for some multidimensional stochastic recursions},
  author={Dariusz Buraczewski and Ewa Damek and Yves Guivarc'h and Andrzej Hulanicki and Roman Urban},
  journal={Probability Theory and Related Fields},
  year={2008},
  volume={145},
  pages={385-420}
}
We consider a stochastic recursion Xn+1 = Mn+1Xn + Qn+1, ($${n\in \mathbb {N}}$$), where (Qn, Mn) are i.i.d. random variables such that Qn are translations, Mn 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… 
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