Notes on Sub-Gaussian Random Elements

2020 ◽  
pp. 197-203
Author(s):  
George Giorgobiani ◽  
Vakhtang Kvaratskhelia ◽  
Vaja Tarieladze
Keyword(s):  
Random Elements

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.

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

Limit theorem for the maximum of dependent Gaussian random elements in a Banach space

1997 ◽  
Vol 49 (7) ◽  
pp. 1129-1133 ◽  
Author(s):  
V. A. Koval’ ◽  
R. Schwabe
Keyword(s):  
Banach Space ◽  
Limit Theorem ◽  
Random Elements

On the Rate of Complete Convergence for Weighted Sums of Arrays of Banach Space Valued Random Elements

2003 ◽  
Vol 47 (3) ◽  
pp. 455-468 ◽  
Author(s):  
T. C. Hu ◽  
D. Li ◽  
A. Rosalsky ◽  
A. I. Volodin
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Random Elements

scholarly journals Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces

2018 ◽  
Vol 45 (3) ◽  
pp. 555-570
Author(s):  
Nguyen Tran Thuan ◽  
Nguyen Van Quang
Keyword(s):  
Metric Spaces ◽  
Random Elements

scholarly journals The space $D$ in several variables: random variables and higher moments

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Random Variables ◽  
Higher Moments ◽  
Multilinear Form ◽  
Standard Case ◽  
Random Functions ◽  
Several Variables ◽  
Random Elements ◽  
Point Evaluations

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $\sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.

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