Remarks on the Convergence of Series of Independent Random Elements with Values in the Spaces $l_p, 1 \leqq p < + \infty $

1977 ◽  
Vol 21 (2) ◽  
pp. 386-388 ◽  
Author(s):  
Nguyen Xuy Tien
Keyword(s):  
Convergence Of Series ◽  
Random Elements

On convergence of series of independent random elements in banach spaces

1999 ◽  
Vol 17 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Eunwoo Nam ◽  
Andrew Rosalsky ◽  
Andrej I. Volodin
Keyword(s):  
Banach Spaces ◽  
Convergence Of Series ◽  
Random Elements

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

2001 ◽  
Vol 8 (2) ◽  
pp. 377-388
Author(s):  
Andrew Rosalsky ◽  
Andrei I. Volodin
Keyword(s):  
Banach Space ◽  
Convergent Series ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Nonlinear Anal ◽  
Convergence Of Series ◽  
Special Cases ◽  
Random Elements ◽  
Maximal Moment ◽  
Martingale Convergence

Abstract 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 [Teor. Īmovīr. ta Mat. Statist. 52: 120–131, 1995] and Rosalsky and Rosenblatt [Bull. Inst. Math. Acad. Sinica 11: 185–208, 1983, Nonlinear Anal. 30: 4237–4248, 1997].

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. Correction

2003 ◽  
Vol 10 (4) ◽  
pp. 799-802
Author(s):  
Andrew Rosalsky ◽  
Andrei I. Volodin
Keyword(s):  
Acta Math ◽  
Convergence Of Series ◽  
Corrected Version ◽  
Random Elements ◽  
Maximal Moment ◽  
Martingale Convergence

Abstract A result by Móricz, Su, and Taylor from Acta Math. Hungar. 65(1994), 1–16, was misstated in the authors' paper in Georgian Math. J. 8(2001), No. 2, 377–388, where due to this misstatement the invalid formulation and proof of a corollary is given. In this correction note, the needed result is correctly stated and a corrected version of the invalid corollary is proved.

scholarly journals Complete convergence for sums of arrays of random elements

2000 ◽  
Vol 23 (11) ◽  
pp. 789-794 ◽  
Author(s):  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Moment Conditions ◽  
Random Elements ◽  
Rowwise Independent

Let{Xni}be an array of rowwise independentB-valued random elements and{an}constants such that0<an↑∞. Under some moment conditions for the array, it is shown that∑i=1nXni/anconverges to0completely if and only if∑i=1nXni/anconverges to0in probability.

Convergence of Series in Mittag-Leffler Type Functions

2010 ◽  
Author(s):  
J. Paneva-Konovska ◽  
Michail D. Todorov ◽  
Christo I. Christov
Keyword(s):  
Convergence Of Series

Some mean convergence theorems for weighted sums of Banach space valued random elements

Stochastics ◽  
2021 ◽  
pp. 1-19
Author(s):  
Pingyan Chen ◽  
Manuel Ordóñez Cabrera ◽  
Andrew Rosalsky ◽  
Andrei Volodin
Keyword(s):  
Banach Space ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Mean Convergence ◽  
Random Elements

On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements

2002 ◽  
Vol 47 (3) ◽  
pp. 533-547 ◽  
Author(s):  
Tien-Chung Hu ◽  
Tien-Chung Hu ◽  
Deli Li ◽  
Deli Li ◽  
Andrew Rosalsky ◽  
...  
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Random Elements
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