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A limit theorem for randomly stopped independent increment processes on separable metrizable groups |
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| Authors: | Peter Becker–Kern Gyula Pap |
| Institution: | 1. Fachbereich Mathematik, Universit?t Dortmund, 44221 Dortmund, GermanyPhone: +49 231 755 3099, Fax: +49 231 755 3064;2. Faculty of Informatics, University of Debrecen, Pf. 12, H–4010 Debrecen, Hungary;3. Phone: +36 52 316666 22826, Fax: +36 52 416857 |
| Abstract: | In the spirit of the classical random central limit theorem a general limit theorem for random stopping in the scheme of infinitesimal triangular arrays on a separable metrizable group is presented. The approach incorporates and generalizes earlier results for normalized sequences of independent random variables on both separable Banach spaces and simply connected nilpotent Lie groups originated by Siegel and Hazod, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| Keywords: | Random product infinitesimal triangular array Ré nyi‐mixing asymptotic independence Anscombe condition integral mixture semi‐stable hemigroup separable Banach space simply connected nilpotent Lie group |