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References
D. Aldous, Stopping times and tightness, Ann. Probab., 6 (1978), pp. 335–340.
N. H. Bingham, Random walks on spheres, Z. Wahrsch. Verw. Geb., 22 (1972), pp. 169–192.
H. Chébli, Opérateurs de translation généralisée et semigroupes de convolution, in: Théorie du Potentiel et Analyse Harmonique, Lect. Notes. Math., Springer, 404 (1974), pp. 35–59.
U. Finckh, Beiträge zur Wahrscheinlichkeitstheorie auf einer Kingman-Struktur, Dissertation, Tübingen, 1986.
J. Flensted-Jensen and T. H. Koornwinder, The convolution structure for Jacobi function expansions, Ark. Mat., 11 (1973), pp. 245–262.
L. Gallardo, Comportement asymptotique des marches aléatoires associées aux polynômes de Gegenbauer et applications, Adv. Appl. Probab., 16 (1984), pp. 293–323.
L. Gallardo and V. Ries, La loi des grands nombres pour les marches aléatoires sur le dual de SU (2), Stud. Math., LXVI (1979), pp. 93–105.
G. Gasper, Positivity and the convolution structure for Jacobi Series, Ann. Math., 93 (1971), pp. 112–118.
H. Heyer, Probability theory on hypergroups: a survey, in: Probability Measures on Groups VII, Lect. Not. Math., Springer, 1064 (1984), pp. 481–550.
H. Heyer, Convolution semigroups and potential kernels on a commutative hypergroup, in: The Analytical and Topological Theory of Semigroups, De Gruyter Expositions in Math., 1 (1990), pp. 279–312.
R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math., 18 (1975), pp. 1–101.
B. M. Levitan, On a class of solutions of the Kolmogorov-Smolukhinski equation, Vestn. Leningrad. Univ., 7 (1960), pp. 81–115.
M. Mabrouki, Principe d'invariance pour les marches aléatoires associées aux polynômes de Gegenbauer et applications, C. R. Acad. Sci., Paris, 299 (1984), pp. 991–994.
K. Trimèche, Probabilités indéfiniment divisibles et théorème de la limite centrale pour une convolution généralisée sur la demi-droite, C. R. Acad. Sci., Paris, 286 (1978).
M. Voit, Central limit theorems for random walks on No that are associated with orthogonal polynomials, J. Mult. Anal., 34 (1990), pp. 290–322.
M. Voit, Central limit theorems for a class of polynomial hypergroups, Adv. Appl. Probab., 22 (1990), pp. 68–87.
Hm. Zeuner, On hyperbolic hypergroups, in: Probability Measures on Groups VIII, Lect. Not. Math., Springer, 1210 (1986), pp. 216–224.
Hm. Zeuner, Laws of large numbers of hypergroups on R+, Math. Ann., 283 (1989), pp. 657–678.
Hm. Zeuner, The central limit theorem for Chébli-Trimèche hypergroups, J. Theoret. Prob., 2 (1989), pp. 51–63.
Hm. Zeuner, Limit theorems for one-dimensional hypergroups, Habilitationsschrift, Tübingen, 1990.
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Heyer, H. (1993). Functional limit theorems for random walks on one-dimensional hypergroups. In: Kalashnikov, V.V., Zolatarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084481
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DOI: https://doi.org/10.1007/BFb0084481
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