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On Complete Convergence for Arrays of Random Elements and Variables |
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| Authors: | Víctor Hernández Andrei Volodin |
| Institution: | 1. Departamento de Estadística e Investigación Operativa , de la Universidad Nacional de Educación a Distancia , Madrid, Spain;2. Department of Mathematics and Statistics , University of Regina , Regina, Saskatchewan, Canada |
| Abstract: | Abstract We obtain complete convergence results for arrays of row-wise independent Banach space valued random elements. The main result deals with two cases that usually are considered separately: when no assumptions are made concerning the geometry of the underlying Banach space and when the Banach space is of Rademacher type p. |
| Keywords: | Array of Banach space valued random elements Complete conver-gence Convergence in probability Domination conditions Normed partial sums Row-wise independence Type p Banach space |