Domains of attraction with inner norming on Sturm-Liouville hypergroups

Hm. Zeuner

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

Full text of the article:

• Compressed PostScript file (154 kilobytes)
• PDF file (233 kilobytes)