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Domains of Attraction with Inner Norming on Sturm–Liouville Hypergroups
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H. M. Zeuner
Published/Copyright:
June 3, 2010
Abstract
In this article we study the convergence of convolution powers of normalized measures (θCnν)*n on a Sturm–Liouville hypergroup (ℝ+,∗). It is shown that this sequence converges for a suitable choice of the normalizing constants cn > 0 if and only if the usual regular variation conditions of the tail of ν are valid. The possible limit distributions are described in terms of their Fourier transform; they form a two dimensional family of probability measures on ℝ+.
Key words and phrases.: Domain of attraction; stable measure; randomized sum; random walk; Sturm–Liouville hypergroup
Published Online: 2010-06-03
Published in Print: 1995-December
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Keywords for this article
Domain of attraction;
stable measure;
randomized sum;
random walk;
Sturm–Liouville hypergroup
Articles in the same Issue
- An Alternative Model of the General Relativity Theory
- Nonlinear Contractions on Semimetric Spaces
- On Weakly Darboux Functions and Some Problem Connected with the Morrey Monotonicity
- On Translations of Sets and Functions
- Global Existence of Solutions for Dirichlet Problem to Nonlinear Diagonal Parabolic System with Maximal Growth Conditions
- On Affine Selections of Set–Valued Functions
- Coinitial Families of Perfect Sets
- Fixed Point and Approximate Fixed Point Theorems for Non–Affine Maps
- Domains of Attraction with Inner Norming on Sturm–Liouville Hypergroups
