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Edgeworth expansion on n-spheres and Jacobi hypergroups

Published online by Cambridge University Press:  17 April 2009

Gyula Pap  and
Michael Voit
Gyula Pap
Affiliation:
Institute of Mathematics, Lajos Kossuth University of Debrecen, Egyetem tér 10, H–4010 Debrecen, Hungary e-mail: papgy@math.klte.hu
Michael Voit
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D–72076 Tübingen, Germany e-mail: voit@uni-tuebingen.de
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 393 - 401
Copyright
Copyright © Australian Mathematical Society 1998

References

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