Limit theorems on locally compact Abelian groups |
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| Authors: | Mátyás Barczy Alexander Bendikov Gyula Pap |
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| Affiliation: | 1. Faculty of Informatics, University of Debrecen, Pf. 12, H–4010 Debrecen, Hungary;2. Phone: +36 52 512 900 / 22804, Fax: +36 52 416 857;3. Mathematical Institute, Wroclaw University, pl. Grundwaldzki 2/4, 50‐384 Wroclaw, Poland;4. Phone: +48 71 3 28 07 17, Fax: +48 71 3 20 44 29 |
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| Abstract: | We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem 4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem gives sufficient conditions for convergence of the row sums, but the limit measure cannot have a nondegenerate idempotent factor. Then we prove necessary and sufficient conditions for convergence of the row sums, where the limit measure can be also a nondegenerate Haar measure on a compact subgroup. Finally, we investigate special cases: the torus group, the group of p ‐adic integers and the p ‐adic solenoid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | (Central) limit theorems on locally compact Abelian groups torus group group of p ‐adic integers p ‐adic solenoid |
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