Regular behavior at infinity of stationary measures of stochastic recursion on NA groups

• Autorzy: Dariusz Buraczewski , Ewa Damek
• Języki publikacji: EN

Abstrakty

EN

Let N be a simply connected nilpotent Lie group and let $S = N ⋊ (ℝ⁺)^{d}$ be a semidirect product, $(ℝ⁺)^{d}$ 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 = MₙX_{n-1} + Qₙ. We prove that for an appropriate homogeneous norm on N there is χ₀ such that
$lim_{t→∞} t^{χ₀}ν{x: |x| > t} = C > 0$.
In particular, this applies to classical Poisson kernels on symmetric spaces, bounded homogeneous domains in ℂⁿ or homogeneous manifolds of negative curvature.

Kategorie tematyczne

• 22E25: Nilpotent and solvable Lie groups
• 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
• 60J50: Boundary theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 499-523

Daty

wydano

2010

Twórcy

autor

Dariusz Buraczewski

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Ewa Damek

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland

Identyfikatory

DOI

10.4064/cm118-2-8