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### Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap

Applications of Mathematics

Let $\left\{{X}_{n,j},1\le j\le m\left(n\right),n\ge 1\right\}$ be an array of rowwise pairwise negative quadrant dependent mean 0 random variables and let $0<{b}_{n}\to \infty$. Conditions are given for ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}/{b}_{n}\to 0$ completely and for ${max}_{1\le k\le m\left(n\right)}|{\sum }_{j=1}^{k}{X}_{n,j}|/{b}_{n}\to 0$ completely. As an application of these results, we obtain a complete convergence theorem for the row sums ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}^{*}$ of the dependent bootstrap samples $\left\{\left\{{X}_{n,j}^{*},1\le j\le m\left(n\right)\right\},n\ge 1\right\}$ arising from a sequence of i.i.d. random variables $\left\{{X}_{n},n\ge 1\right\}$.

### 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”.

### A generalization of the global limit theorems of R. P. Agnew.

International Journal of Mathematics and Mathematical Sciences

### Addendum: A generalization of the global limit theorems of R. P. Agnew.

International Journal of Mathematics and Mathematical Sciences

### A survey of limit laws for bootstrapped sums.

International Journal of Mathematics and Mathematical Sciences

### On the weak law of large numbers for normed weighted sums of i.i.d. random variables.

International Journal of Mathematics and Mathematical Sciences

### Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables.

International Journal of Mathematics and Mathematical Sciences

### 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

### Strong laws of large numbers for weighted sums of random elements in normed linear spaces.

International Journal of Mathematics and Mathematical Sciences

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