How a centred random walk on the affine group goes to infinity
Brofferio, Sara1
1 Technische Universität Graz Institut für Mathematik C Steyergasse 30 A-8010 Graz (Austria)
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 3, pp. 371-384.
DOI : 10.1016/S0246-0203(02)00015-8
Brofferio, Sara 1

1 Technische Universität Graz Institut für Mathematik C Steyergasse 30 A-8010 Graz (Austria) 
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Brofferio, Sara. How a centred random walk on the affine group goes to infinity. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 3, pp. 371-384. doi : 10.1016/S0246-0203(02)00015-8. http://archive.numdam.org/articles/10.1016/S0246-0203(02)00015-8/

[1] M. Babillot, P. Bougerol, L. Elie, The random difference equation Xn=AnXn−1+Bn in the critical case, Ann. Probab. 25 (1) (1997) 478-493. | Zbl

[2] D.I. Cartwright, V.A. Kaĭmanovich, W. Woess, Random walks on the affine group of local fields and of homogeneous trees, Ann. Inst. Fourier (Grenoble) 44 (4) (1994) 1243-1288. | Numdam | MR | Zbl

[3] L. Élie, Comportement asymptotique du noyau potentiel sur les groupes de Lie, Ann. Sci. École Norm. Sup. (4) 15 (2) (1982) 257-364. | Numdam | MR | Zbl

[4] R.F. Engle, T. Bollerslev, Modelling the persistence of conditional variances, Econometric Rev. 5 (1) (1986) 1-87, With comments and a reply by the authors. | MR | Zbl

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

[6] C.M. Goldie, R.A. Maller, Stability of perpetuities, Ann. Probab. 28 (3) (2000) 1195-1218. | MR | Zbl

[7] A.K. Grincevičius, A central limit theorem for the group of linear transformations of the line, Dokl. Akad. Nauk SSSR 219 (1974) 23-26. | MR | Zbl

[8] Y. Guivarc'H, M. Keane, B. Roynette, Marches aléatoires sur les groupes de Lie, Lecture Notes in Math., 624, Springer-Verlag, Berlin, 1977. | MR | Zbl

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

[10] É. Le Page, M. Peigné, A local limit theorem on the semi-direct product of R∗+ and Rd, Ann. Inst. H. Poincaré Probab. Statist. 33 (2) (1997) 223-252. | Numdam | Zbl

[11] D.F. Nicholls, B.G. Quinn, Random Coefficient Autoregressive Models: An Introduction, Lecture Notes in Physics, 151, Springer-Verlag, New York, 1982. | MR | Zbl

[12] D. Revuz, Markov Chains, North-Holland Mathematical Library, 11, North-Holland, Amsterdam, 1975. | MR | Zbl

[13] W. Vervaat, On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables, Adv. Appl. Probab. 11 (4) (1979) 750-783. | MR | Zbl

[14] Yor M. (Ed.), Exponential Functionals and Principal Values Related to Brownian Motion, Revista Matemática Iberoamericana, Madrid, 1997, A collection of research papers. | MR | Zbl

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