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

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

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 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.

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

Sign in / Sign up

Export Citation Format

Share Document