EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 1, No. 2, pp. 213-221 (1995)

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Domains of attraction with inner norming on Sturm-Liouville hypergroups

Hm. Zeuner

Fachbereich Mathematik
der Universität Dortmund
Vogelpothsweg 87
D-44221 Dortmund
Federal Republic of Germany
email: hmz@mathematik.uni-dortmund.de

Abstract: In this article we study the convergence of convolution powers of normalized measures $(\theta_{c_n}\nu)^{*n}$ on a Sturm--Liouville hypergroup $(\RP,*)$. It is shown that this sequence converges for a suitable choice of the normalizing constants $c_n>0$ if and only if the usual regular variation conditions of the tail of $\nu$ are valid. The possible limit distributions are described in terms of their Fourier transform; they form a two dimensional family of probability measures on $\RP$.

Keywords: Domain of attraction, stable measure,randomized sum, random walk, Sturm-Liouville hypergroup

Classification (MSC2000): 60E07, 60F05, 43A62; 60B10, 60B15, 60J15

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Electronic fulltext finalized on: 29 May 2002. This page was last modified: 21 Dec 2002.

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