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

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 ${L}^{2}\left(\Omega ,ℱ,ℙ\right)$ 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 ${L}^{2}\left(\Omega ,ℱ,ℙ\right)$) to be orthogonal to some other sequence in ${L}^{2}\left(\Omega ,ℱ,ℙ\right)$. The result obtained is interesting...

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

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 ($m=1,2,\cdots$). For a sequence of $m$-linearly negative quadrant dependent random variables $\left\{{X}_{n},n\ge 1\right\}$ and $1 (resp. $1\le p<2$), conditions are provided under which ${n}^{-1/p}{\sum }_{k=1}^{n}\left({X}_{k}-E{X}_{k}\right)\to 0$ in ${L}^{1}$ (resp. in ${L}^{p}$). Moreover, for $1\le p<2$, conditions are provided under which ${n}^{-1/p}{\sum }_{k=1}^{n}\left({X}_{k}-E{X}_{k}\right)$ 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”

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.

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.

Georgian Mathematical Journal

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

Lobachevskii Journal of Mathematics

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

International Journal of Mathematics and Mathematical Sciences

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

Lobachevskii Journal of Mathematics

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