no. 2
A local limit theorem on the semi-direct product of ℝ *+ and ℝ d
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 223-252 
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     title = {A local limit theorem on the semi-direct product of $\mathbb {R}^{*+}$ and $\mathbb {R}^d$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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Le Page, Émile; Peigné, Marc. A local limit theorem on the semi-direct product of $\mathbb {R}^{*+}$ and $\mathbb {R}^d$. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 223-252. https://www.numdam.org/item/AIHPB_1997__33_2_223_0/

[1] V.I. Afanas'Ev, On a maximum of a transient random walk in random environment, Theory Prob. Appl., Vol. 35, n° 2, 1987, pp. 205-215. | Zbl | MR

[2] M. Babillot, Ph. Bougerol and L. Elie, The random difference equation Xn = AnXn-1 + Bn in the critical case, to appear in Annals of Probability. | Zbl

[3] N.H. Bingham, Limit theorem in fluctuation theory, Adv. Appl. Prob., Vol. 5, 1973, pp. 554-569. | Zbl | MR

[4] Ph. Bougerol, Théorème central limite local sur certains groupes de Lie, Ann. Scient. Ec. Norm. Sup., 4e série, T. 14, 1981, pp. 403-432. | Zbl | MR | Numdam

[5] Ph. Bougerol, Exemples de théorèmes locaux sur les groupes résolubles, Ann. I.H.P., Vol. XIX, n° 4, 1983, pp. 369-391. | Zbl | MR | Numdam

[6] L. Breiman, Probability, Addison-Wesley Publishing Company, 1964. | Zbl | MR

[7] L. Elie, Marches aléatoires: théorie du renouvellement, Thèse de Doctorat d'État, Université Paris VII, 1981.

[8] W. Feller, An introduction to probability theory and its applications, Vol. 2, 2nd edition, 1971, J. Wiley, New York. | Zbl | MR

[9] H. Furstenberg, Translation-invariant cones of functions on semi-simple Lie groups, Bull. of the A.M.S, Vol. 71, n° 2, 1965, pp. 271-326. | Zbl | MR

[10] A.K. Grincevicius, A central limit theorem for the group of linear transformation of the real axis, Soviet Math. Doklady, Vol. 15, n° 6, 1974, pp. 1512-1515. | Zbl

[11] Y. Guivarc'H, Théorèmes quotients pour les marches aléatoires, Astérisque, Vol. 74, 1980, S.M.F., pp. 15-28. | Zbl | MR | Numdam

[12] Y. Guivarc'H et Q. Liu, Sur la probabilité de survie d'un processus de branchement dans un environnement aléatoire (in preparation).

[13] Iglehart, Random walks with negative drift conditioned to stay positive, J. Appl Prob., Vol. 11, 1974, pp. 742-751. | Zbl | MR

[14] M.V. Kozlov, On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment, Theory Prob. Appl., Vol. 21, n° 4, 1976, pp. 791-804. | Zbl | MR

[15] E. Le Page and M. Peigné, Exemples de théorèmes locaux pour certains noyaux de transition, Journées Fortet du 1er juin 1995, to appear in Editions Hermès. | MR

[16] F. Spitzer, Principles of random walks, D. Van Nostrand Company, 1964. | Zbl

[17] N.Th. Varopoulos, Wiener-Hopf theory and nonunimodular groups, J. of Funct. Anal., Vol. 120, 1994, pp. 467-483. | Zbl | MR

[18] N.Th. Varopoulos, Diffusion on Lie groups, Can. J. Math., Vol. 46, 1994, pp. 438-448. | Zbl | MR

[19] N.Th. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and geometry groups, Cambridge Tracts in Math., n° 100, 1993. | MR