Let N be a simply connected nilpotent Lie group and let be a semidirect product, acting on N by diagonal automorphisms. Let (Qₙ,Mₙ) be a sequence of i.i.d. random variables with values in S. Under natural conditions, including contractivity in the mean, there is a unique stationary measure ν on N for the Markov process Xₙ = MₙXn-1 + Qₙ. We prove that for an appropriate homogeneous norm on N there is χ₀ such that . In particular, this applies to classical Poisson kernels on symmetric spaces, bounded homogeneous domains in ℂⁿ or homogeneous manifolds of negative curvature.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-8,
author = {Dariusz Buraczewski and Ewa Damek},
title = {Regular behavior at infinity of stationary measures of stochastic recursion on NA groups},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {499-523},
zbl = {1191.60011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-8}
}
Dariusz Buraczewski; Ewa Damek. Regular behavior at infinity of stationary measures of stochastic recursion on NA groups. Colloquium Mathematicae, Tome 120 (2010) pp. 499-523. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-8/