Semigroups in Probability Theory

  • Paul Ressel


Semigroups are very natural and general structures and enter our mathematical life from the very beginning (N with respect to addition, multiplication, maximum or minimum, sets with respect to union or intersection). Due to their simple axioms they are very often and easily found. If M is a nonempty set and S = M M is the set of all mappings from M to M, then S is a semigroup with respect to composition, and in fact every semigroup can be realized as a subsemi-group of M M for some M.


Point Process Random Measure Positive Definite Matrix Positive Definiteness Neutral Element 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Berg, C. (1990). Positive definite and related functions on semigroups. In “The Analytical and Topological Theory of Semigroups” (Eds. K. H. Hofmann, J.D. Lawson, J.S. Pym), pp. 253–278. Berlin — New York: Walter de Gruyter & Co.Google Scholar
  2. [2]
    Berg, C., J.P.R. Christensen and P. Ressel (1984). Harmonic Analysis on Semigroups. Graduate Texts in Mathematics, Vol. 100. Berlin — Heidelberg-New York: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  3. [3]
    Bickel, P. J. and W.R. Van Zwet (1980). On a theorem of Hoeffding. In Asymptotic Theory of Statistical Tests and Estimation. (Ed. by I.M. Chakravarti), pp. 307–324. New York: Academic Press.Google Scholar
  4. [4]
    Bisgaard, T.M. (1990). Hoeffding’s inequalities: A counterexample. J. Theoretical Probability 3, 71–80.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Buchwalter, H. (1986). Les fonctions de Lévy existent! Math. Ann. 274, 31–34.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Choquet, G. (1986). Une démonstration du théorème de Bochner-Weil par discrétisation du groupe. Results in Mathematics 9, 1–9.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Lauritzen, S.L. (1984). Extreme point models in statistics. Scand. J. Statistics 11, 65–91.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Lauritzen, S.L. (1988). Extremal families and systems of sufficient statistics. Lecture Notes in Statistics 49. Berlin — Heidelberg — New York: Springer Verlag.zbMATHCrossRefGoogle Scholar
  9. [9]
    Ressel, P. (1982). A general Hoeffding type inequality. Z. Wahrsch. verw. Gebiete 61, 223–235.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Ressel, P. (1985). De Finetti-type theorems: an analytical approach. Ann. Prob. 13, 898–922.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Ressel, P. (1988). Integral representations for distributions of symmetric stochastic processes. Prob. Th. Rel. Fields 79, 451–467.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Ressel, P. (1989). A conjecture concerning mixtures of characters from a given closed subsemigroup in the dual. In “Probability Measures on Groups IX” (Ed. H. Heyer). Lecture Notes in Mathematics 1379, pp. 299–309. Berlin — Heidelberg — New York: Springer-Verlag.CrossRefGoogle Scholar
  13. [13]
    Ressel, P. and W. Schmidtchen (1991). A new characterization of Laplace functionals and probability generating functionals. Prob. Th. Rel. Fields &, 195–213.Google Scholar
  14. [14]
    Ruzsa, I.Z. and G.J. Székely (1988). Algebraic Probability Theory. Chichester — New York: John Wiley & Sons.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Paul Ressel
    • 1
  1. 1.Katholische Universität EichstättEichstättGermany

Personalised recommendations