On tails of stationary measures on a class of solvable groups

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1. [1] R. Azencott, E. Wilson, On homogeneous manifolds with negative curvature, part I, Trans. Amer. Math. Soc.215 (1976) (1976) 323-362. Zbl0293.53017MR394507
2. [2] D. Buraczewski, E. Damek, Y. Guivarc'h, A. Hulanicki, R. Urban, On tail properties of stochastic recursions connected with generalized rigid motions, preprint. 
3. [3] D. Buraczewski, E. Damek, A. Hulanicki, Asymptotic behavior of Poisson kernels NA group, Comm. Partial Differential Equations31 (2006) 1547-1589. Zbl1109.22005MR2273965
4. [4] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math.89 (1988) 169-196. Zbl0675.22005MR955662
5. [5] E. Damek, A. Hulanicki, Boundaries for leftinvariant subelliptic operators on semidirect products of nilpotent and Abelian groups, J. Reine Angew. Math.411 (1990) 1-38. Zbl0699.22012MR1072971
6. [6] E. Damek, A. Hulanicki, Asymptotic behavior of the invariant measure for a diffusion related to a NA group, Colloq. Math.104 (2006) 285-309. Zbl1087.22006MR2197079
7. [7] B. de Saporta, Y. Guivarc'h, E. Le Page, On the multidimensional stochastic equation $Y_{n+1}=A_n{Y}_n+B_n$, C. R. Math. Acad. Sci. Paris339 (7) (2004) 499-502. Zbl1063.60099MR2099549
8. [8] J. Faraut, A. Korányi, Analysis on Symmetric Cones, Clarendon Press, Oxford, 1994. Zbl0841.43002MR1446489
9. [9] W. Feller, An Introduction to Probability Theory and its Application II, John Wiley and Sons, New York, 1966. Zbl0138.10207MR210154
10. [10] G.B. Folland, E.M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, NJ, 1982. Zbl0508.42025MR657581
11. [11] Ch.M. Goldie, Implicit renewal theory and tails of solutions of random equations, Ann. Appl. Probab.1 (1) (1991) 126-166. Zbl0724.60076MR1097468
12. [12] A.K. Grincevičius, On limit distribution for a random walk on the line, Lithuanian Math. J.15 (1975) 580-589. Zbl0373.60009
13. [13] A.K. Grincevičius, Products of random affine transformations, Lithuanian Math. J.20 (1980) 279-282. Zbl0472.60035MR605960
14. [14] Y. Guivarc'h, Heavy tail properties of multidimensional stochastic recursions, in: Dynamics & Stochastic, IMS Lecture Notes Monograph Series, vol. 48, 2006, pp. 85-99. Zbl1126.60052MR2306191
15. [15] W. Hebisch, A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math.96 (3) (1990) 231-236. Zbl0723.22007MR1067309
16. [16] E. Heintze, On homogeneous manifolds of negative curvature, Math. Ann.211 (1974) 23-34. Zbl0273.53042MR353210
17. [17] H. Kesten, Random difference equations and renewal theory for products of random matrices, Acta Math.131 (1973) 207-248. Zbl0291.60029MR440724
18. [18] C. Klüppelberg, S. Pergamenchtchikov, The tail of the stationary distribution of a random coefficient AR(q) model, Ann. Appl. Probab.14 (2) (2004) 971-1005. Zbl1094.62114MR2052910
19. [19] É. Le Page, Théorème de renouvellement pour les produits de matrices aléatoires et les équations aux différences aléatoires, in: Séminaires de probabilités Rennes 1983, Univ. Rennes I, Rennes, 1983, 116 pp. MR863321
20. [20] I.I. Piatetski-Shapiro, Geometry of Classical Domains and Theory of Automorphic Functions, Sovremennye Problemy Matematiki, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961. Zbl0137.27502MR136770
21. [21] A. Raugi, Fonctions harmoniques sur les groupes localment compact a base denomerable, Bull. Soc. Math. France Mém.54 (1977) 5-118. Zbl0389.60003MR517392