EUDML

Currently displaying 1 – 9 of 9

Order by Relevance | Title | Year of publication

On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

Umberto Triacca; Andrei Volodin — 2010

Applications of Mathematics

This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space $L^{2} (Ω, ℱ, ℙ)$ of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of $L^{2} (Ω, ℱ, ℙ)$ ) to be orthogonal to some other sequence in $L^{2} (Ω, ℱ, ℙ)$ . The result obtained is interesting...

Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables

Yongfeng Wu; Andrew Rosalsky; Andrei Volodin — 2013

Applications of Mathematics

The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of $m$ -linearly negative quadrant dependent random variables ( $m = 1, 2, \dots$ ). For a sequence of $m$ -linearly negative quadrant dependent random variables ${X_{n}, n \geq 1}$ and $1 < p < 2$ (resp. $1 \leq p < 2$ ), conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k}) \to 0$ in $L^{1}$ (resp. in $L^{p}$ ). Moreover, for $1 \leq p < 2$ , conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k})$ converges completely to $0$ . The current work extends some results of Pyke and Root (1968) and it extends and improves some...

A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”

Yongfeng Wu; Andrew Rosalsky; Andrei Volodin — 2017

Applications of Mathematics

The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”.

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.

Rosalsky, Andrew; Volodin, Andrei I. — 2001

Georgian Mathematical Journal

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.

Rosalsky, Andrew; Volodin, Andrei I. — 2003

Georgian Mathematical Journal

Limiting behaviour of moving average processes based on a sequence of $ρ^{-}$ mixing and negatively associated random variables.

Budsaba, Kamon; Chen, Pingyan; Volodin, Andrei — 2007

Lobachevskii Journal of Mathematics

On the rate of convergence of bootstrapped means in a Banach space.

Ejaz Ahmed, S.; Hu, T.-C.; Volodin, Andrei I. — 2001

International Journal of Mathematics and Mathematical Sciences

On the asymptotic probability for the deviations of dependent bootstrap means from the sample mean.

Ahmed, S.Ejaz; Li, Deli; Rosalsky, Andrew; Volodin, Andrei — 2005

Lobachevskii Journal of Mathematics

A note on the rate of complete convergence for maximums of partial sums for moving average processes in Rademacher type Banach spaces.

Chen, Pingyan; Hu, Tien-Chung; Volodin, Andrei — 2006

Lobachevskii Journal of Mathematics

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 9 of 9

On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables

A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”

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.

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.

Limiting behaviour of moving average processes based on a sequence of $ρ^{-}$ mixing and negatively associated random variables.

On the rate of convergence of bootstrapped means in a Banach space.

On the asymptotic probability for the deviations of dependent bootstrap means from the sample mean.

A note on the rate of complete convergence for maximums of partial sums for moving average processes in Rademacher type Banach spaces.