Advertisement

Functional limit theorems for random walks on one-dimensional hypergroups

  • Herbert Heyer
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1546)

Keywords

Central Limit Theorem Moment Function Invariance Principle Bessel Process Convolution Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Aldous, Stopping times and tightness, Ann. Probab., 6 (1978), pp. 335–340.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    N. H. Bingham, Random walks on spheres, Z. Wahrsch. Verw. Geb., 22 (1972), pp. 169–192.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    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.CrossRefzbMATHGoogle Scholar
  4. [4]
    U. Finckh, Beiträge zur Wahrscheinlichkeitstheorie auf einer Kingman-Struktur, Dissertation, Tübingen, 1986.zbMATHGoogle Scholar
  5. [5]
    J. Flensted-Jensen and T. H. Koornwinder, The convolution structure for Jacobi function expansions, Ark. Mat., 11 (1973), pp. 245–262.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    L. Gallardo, Comportement asymptotique des marches aléatoires associées aux polynômes de Gegenbauer et applications, Adv. Appl. Probab., 16 (1984), pp. 293–323.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    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.Google Scholar
  8. [8]
    G. Gasper, Positivity and the convolution structure for Jacobi Series, Ann. Math., 93 (1971), pp. 112–118.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Heyer, Probability theory on hypergroups: a survey, in: Probability Measures on Groups VII, Lect. Not. Math., Springer, 1064 (1984), pp. 481–550.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    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.MathSciNetzbMATHGoogle Scholar
  11. [11]
    R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math., 18 (1975), pp. 1–101.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    B. M. Levitan, On a class of solutions of the Kolmogorov-Smolukhinski equation, Vestn. Leningrad. Univ., 7 (1960), pp. 81–115.MathSciNetzbMATHGoogle Scholar
  13. [13]
    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.MathSciNetzbMATHGoogle Scholar
  14. [14]
    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).zbMATHGoogle Scholar
  15. [15]
    M. Voit, Central limit theorems for random walks on No that are associated with orthogonal polynomials, J. Mult. Anal., 34 (1990), pp. 290–322.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. Voit, Central limit theorems for a class of polynomial hypergroups, Adv. Appl. Probab., 22 (1990), pp. 68–87.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Hm. Zeuner, On hyperbolic hypergroups, in: Probability Measures on Groups VIII, Lect. Not. Math., Springer, 1210 (1986), pp. 216–224.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Hm. Zeuner, Laws of large numbers of hypergroups on R+, Math. Ann., 283 (1989), pp. 657–678.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Hm. Zeuner, The central limit theorem for Chébli-Trimèche hypergroups, J. Theoret. Prob., 2 (1989), pp. 51–63.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Hm. Zeuner, Limit theorems for one-dimensional hypergroups, Habilitationsschrift, Tübingen, 1990.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Herbert Heyer
    • 1
  1. 1.Math. Inst. Univ. TübingenTübingenGermany

Personalised recommendations