On complete convergence in mean for double sums of independent random elements in Banach spaces
- Autores: Parker R.1, Rosalsky A.1
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Afiliações:
- Department of Statistics
- Edição: Volume 38, Nº 1 (2017)
- Páginas: 177-191
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198871
- DOI: https://doi.org/10.1134/S1995080217010164
- ID: 198871
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Resumo
For a double array of random elements {Tm,n, m ≥ 1, n ≥ 1} in a real separable Banach space X, we study the notion of Tm,n converging completely to 0 in mean of order p where p is a positive constant. This notion is stronger than (i) Tm,n converging completely to 0 and (ii) Tm,n converging to 0 in mean of order p as max{m, n} →∞. When X is of Rademacher type p (1 ≤ p ≤ 2), for a double array of independent mean 0 random elements {Vm,n, m ≥ 1, n ≥ 1} in X and a double array of constants {bm,n, m ≥ 1, n ≥ 1}, conditions are provided under which max1≤k≤m,1≤l≤n||Ʃi=1kƩj=1lVi,j||/bm,n converges completely to 0 in mean of order p. Moreover, these conditions are shown to provide an exact characterization of Rademacher type p (1 ≤ p ≤ 2) Banach spaces. Illustrative examples are provided.
Sobre autores
R. Parker
Department of Statistics
Email: rosalsky@stat.ufl.edu
Estados Unidos da América, Gainesville, FL, 32611-8545
A. Rosalsky
Department of Statistics
Autor responsável pela correspondência
Email: rosalsky@stat.ufl.edu
Estados Unidos da América, Gainesville, FL, 32611-8545