• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.825-836
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• 2015

In this article, we discuss the complete moment convergence for arrays of B-valued random variables. We obtain some new results which improve the corresponding ones of Sung and Volodin [17].

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.545-552
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• 2003

Let X$_1$, X$_2$, … be real valued random variables under linearly negatively quadrant dependent (LNQD). In this paper, we discuss the probability inequality of ennett(1962) and Hoeffding(1963) under some suitable random variables. These results are to extend Theorem A and B to LNQD random variables. Furthermore, let ζdenote the ｐth quantile of the marginal distribution function of the $Ｘ_i$'s which is estimated by a smooth estima te $ζ_{pn}$, on the basis of X$_1$, X$_2$, …$X_n$. We establish a convergence of $ζ_{pn}$, under Hoeffding-type probability inequality of LNQD.

• The Journal of Natural Sciences
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• v.9 no.1
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• pp.57-60
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• 1997

Let {$X_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of rowwise independent B-valued random variables which is uniformly bounded by a random various X satisfying $E|X|^{2p}<\infty$ for some p$\geq$1. Let {$a_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of constants. Under some auxiliary conditions on {$a_{ni}$}, it is shown that $sum_{i=1}^n a_{ni}X_{ni}\rightarrow0$ in probability if and only if $sum_{i=1}^n a_{ni}X_{ni}$ converges completely ot 0.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.255-258
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• 1997

We prove a conjecture of Yu. V. Prokhorov in general Banach Spaces ; let ($X_n$, n$\geq$1} be a sequence of independent identically and symmetrically distributed Banach valued random variables, then the relation $\mid$$\mid$$S_n$$\mid$$\mid$/$b_n$ -> 1 a.s. cannot hold for any choice of constants $b_n$.