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1 results

  • Central limit theorems for a class of polynomial hypergroups

  • Michael Voit
  • Journal:
    Advances in Applied Probability / Volume 22 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    01 July 2016, pp. 68-87
    Print publication:
    March 1990

  • Central limit theorems are proved for random walks on the non-negative integers where the transition probabilities are homogeneous with respect to a sequence of orthogonal polynomials. Assuming some restrictions concerning the three-term recursion formula of these polynomials, one gets a Rayleigh distribution as limit distribution where bounds of the order of convergence can be computed explicitly. These central limit theorems are applied to generalized birth and death random walks and random walks on polynomial hypergroups. Finally some examples of polynomial hypergroups are discussed in view of the limit theorems above.