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Moment inequalities and weak convergence for negatively associated sequences. (English) Zbl 0907.60023

The main results are concerned with sequences of negatively associated random variables. The author proves some upper estimates for $P\left\{|{S}_{n}|\ge \lambda \right\}$, $E|{S}_{n}|$, and $E\left({max}_{1\le n\le k}|{S}_{n}|\right)$, where ${S}_{n}={X}_{1}+\cdots +{X}_{n}$ is the sum of negatively associated random variables. Based on these inequalities a version of the weak invariance principle for strictly stationary negatively associated sequences of random variables is proved. Before proving the invariance principle, the author constructs a sequence of random variables of such a type. Point out the inequality

$E|{S}_{n}{|}^{p}\le {C}_{p}{n}^{p/2-1}\sum _{k=1}^{n}E{|{X}_{k}|}^{p}$

(${C}_{p}$ is a constant depending only upon $p\ge 2$), as a typical result.

##### MSC:
 60E15 Inequalities in probability theory; stochastic orderings 60F05 Central limit and other weak theorems
##### Keywords:
invariance principle; strictly stationary sequence
##### References:
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