On complete convergence in mean for double sums of independent random elements in Banach spaces

2017 ◽  
Vol 38 (1) ◽  
pp. 177-191
Author(s):  
R. Parker ◽  
A. Rosalsky
Keyword(s):  
Banach Spaces ◽  
Complete Convergence ◽  
Random Elements ◽  
Complete Convergence In Mean ◽  
Convergence In Mean

scholarly journals Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces

1997 ◽  
Vol 20 (3) ◽  
pp. 443-450 ◽  
Author(s):  
M. Ordóñez Cabrera
Keyword(s):  
Banach Space ◽  
Recent Result ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Weighted Sum ◽  
Random Elements ◽  
New Hypothesis ◽  
Convergence In Mean

The convergence in mean of a weighted sum∑kank(Xk−EXk)of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the{ank}-compactly uniform integrability of{Xn}. This condition, which is implied by the tightness of{Xn}and the{ank}-uniform integrability of{‖Xn‖}, is weaker than the compactly miform integrability of{Xn}and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.

scholarly journals Mean convergence theorem for multidimensional arrays of random elements in Banach spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-6
Author(s):  
Le Van Thanh
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Multidimensional Arrays ◽  
Stable Type ◽  
Dimensional Array ◽  
Mean Convergence ◽  
Random Elements ◽  
Convergence In Mean

For a d-dimensional array of random elements {Vn,n∈ℤ+d} in a real separable stable type p (1≤p<2) Banach space, a mean convergence theorem is established. Moreover, the conditions for the convergence in mean of order p are shown to completely characterize stable-type p Banach spaces.

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