Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

• 成果类型: Article
• 署名作者: Buraczewski, Dariusz; Damek, Ewa; Guivarc'h, Yves; Hulanicki, Andrzej; Urban, Roman
• 署名单位: University of Wroclaw; Universite de Rennes
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0172-8
• 发表日期: 2009
• 页码: 385-420
• 关键词: Matrices; BEHAVIOR; PRODUCTS

摘要

We consider a stochastic recursion Xn+1 = Mn+1Xn + Q(n+1), (n is an element of N), where (Q(n), M-n) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space R-d and X-n is an element of R-d. In the present paper we show that if the recursion has a unique stationary measure nu with unbounded support then the weak limit of properly dilated. exists and defines a homogeneous tail measure Lambda. The structure of Lambda is studied and the supports of nu and Lambda are compared. In particular, we obtain a product formula for Lambda.