ON CONVERGENCE OF SERIES OF RANDOM ELEMENTS VIA MAXIMAL MOMENT RELATIONS WITH APPLICATIONS TO MARTINGALE CONVERGENCE AND TO CONVERGENCE OF SERIES WITH p-ORTHOGONAL SUMMANDS
نویسندگان
چکیده
The rate of convergence for an almost surely convergent series of Banach space valued random elements is studied in this paper. As special cases of the main result, known results are obtained for a sequence of independent random elements in a Rademacher type p Banach space, and new results are obtained for a martingale difference sequence of random elements in a martingale type p Banach space and for a p-orthogonal sequence of random elements in a Rademacher type p Banach space. The current work generalizes, simplifies, and unifies some of the recent results of Nam and Rosalsky [16] and Rosalsky and Rosenblatt [23, 24]. 2000 Mathematics Subject Classification: 60F05, 60B12, 60B11.
منابع مشابه
CORRECTION ON CONVERGENCE OF SERIES OF RANDOM ELEMENTS VIA MAXIMAL MOMENT RELATIONS WITH APPLICATIONS TO MARTINGALE CONVERGENCE AND TO CONVERGENCE OF SERIES WITH p-ORTHOGONAL SUMMANDS
The authors in their article [2] misstated a result due to Móricz, Su, and Taylor [1]. This misstatement resulted in an invalid formulation and proof of a corollary presented in [2]. In this correction note, the needed result from [1] is correctly stated and a corrected version of the invalid corollary in [2] is proved. 2000 Mathematics Subject Classification: 60F05, 60B12, 60B11.
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