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Published online by Cambridge University Press: 17 April 2009
Suitable normalisation of time-homogeneous rotation-invariant random walks on unit spheres Sd ⊂ ℝd+1 for d ≥ 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is different from the classical case. The proof is performed in the more general setting of Jacobi-type hypergroups on an interval.