On tails of stationary measures on a class of solvable groups
Buraczewski, Dariusz
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007), p. 417-440 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2007__43_4_417_0,
     author = {Buraczewski, Dariusz},
     title = {On tails of stationary measures on a class of solvable groups},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {43},
     year = {2007},
     pages = {417-440},
     doi = {10.1016/j.anihpb.2006.07.002},
     mrnumber = {2329510},
     zbl = {1118.60006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_4_417_0}
}

Buraczewski, Dariusz. On tails of stationary measures on a class of solvable groups. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 417-440. doi : 10.1016/j.anihpb.2006.07.002. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_4_417_0/

[1] R. Azencott, E. Wilson, On homogeneous manifolds with negative curvature, part I, Trans. Amer. Math. Soc. 215 (1976) (1976) 323-362. | MR 394507 | Zbl 0293.53017

[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] D. Buraczewski, E. Damek, A. Hulanicki, Asymptotic behavior of Poisson kernels NA group, Comm. Partial Differential Equations 31 (2006) 1547-1589. | MR 2273965 | Zbl 1109.22005

[4] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988) 169-196. | MR 955662 | Zbl 0675.22005

[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. | MR 1072971 | Zbl 0699.22012

[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. | MR 2197079 | Zbl 1087.22006

[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. Paris 339 (7) (2004) 499-502. | MR 2099549 | Zbl 1063.60099

[8] J. Faraut, A. Korányi, Analysis on Symmetric Cones, Clarendon Press, Oxford, 1994. | MR 1446489 | Zbl 0841.43002

[9] W. Feller, An Introduction to Probability Theory and its Application II, John Wiley and Sons, New York, 1966. | MR 210154 | Zbl 0138.10207

[10] G.B. Folland, E.M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, NJ, 1982. | MR 657581 | Zbl 0508.42025

[11] Ch.M. Goldie, Implicit renewal theory and tails of solutions of random equations, Ann. Appl. Probab. 1 (1) (1991) 126-166. | MR 1097468 | Zbl 0724.60076

[12] A.K. Grincevičius, On limit distribution for a random walk on the line, Lithuanian Math. J. 15 (1975) 580-589. | Zbl 0373.60009

[13] A.K. Grincevičius, Products of random affine transformations, Lithuanian Math. J. 20 (1980) 279-282. | MR 605960 | Zbl 0472.60035

[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. | MR 2306191 | Zbl 1126.60052

[15] W. Hebisch, A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (3) (1990) 231-236. | MR 1067309 | Zbl 0723.22007

[16] E. Heintze, On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974) 23-34. | MR 353210 | Zbl 0273.53042

[17] H. Kesten, Random difference equations and renewal theory for products of random matrices, Acta Math. 131 (1973) 207-248. | MR 440724 | Zbl 0291.60029

[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. | MR 2052910 | Zbl 1094.62114

[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. | MR 863321

[20] I.I. Piatetski-Shapiro, Geometry of Classical Domains and Theory of Automorphic Functions, Sovremennye Problemy Matematiki, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961. | MR 136770

[21] A. Raugi, Fonctions harmoniques sur les groupes localment compact a base denomerable, Bull. Soc. Math. France Mém. 54 (1977) 5-118. | Numdam | MR 517392 | Zbl 0389.60003