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.

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.

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

scholarly journals Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables

1979 ◽  
Vol 2 (2) ◽  
pp. 309-323
Author(s):  
W. J. Padgett ◽  
R. L. Taylor
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Real Numbers ◽  
Martingale Theory ◽  
Random Elements ◽  
Schauder Bases

Let{Xk}be independent random variables withEXk=0for allkand let{ank:n≥1, k≥1}be an array of real numbers. In this paper the almost sure convergence ofSn=∑k=1nankXk,n=1,2,…, to a constant is studied under various conditions on the weights{ank}and on the random variables{Xk}using martingale theory. In addition, the results are extended to weighted sums of random elements in Banach spaces which have Schauder bases. This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.

scholarly journals Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Zdeněk Šmarda ◽  
Yasir Khan ◽  
Qingbiao Wu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Banach Spaces ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Convergence Theorem ◽  
Order Convergence ◽  
Third Order ◽  
The Third

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.

scholarly journals Expectation in metric spaces and characterizations of Banach spaces

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
Artur Bator ◽  
Wiesław Zięba
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Spaces ◽  
Bochner Integral ◽  
Random Elements

AbstractWe consider different definitions of expectation of random elements taking values in metric spaces. All such definitions are valid also in Banach spaces and in this case the results coincide with the Bochner integral. There may exist an isometry between considered metric space and some Banach space and in this case one can use the Bochner integral instead of expectation in metric space. We give some conditions which ensure existence of such isometry, for two different definitions of expectation in metric space.

Sign in / Sign up

Export Citation Format

Share Document