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ON THE CONVERGENCE OF SERIES OF MARTINGALE DIFFERENCES WITH MULTIDIMENSIONAL INDICES
SON, TA CONG,THANG, DANG HUNG Korean Mathematical Society 2015 대한수학회지 Vol.52 No.5
Let {Xn; $n{\succeq}1$} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides conditions under which the series ${\sum}_{i{\preceq}n}\;Xi$ converges almost surely and the tail series {$Tn={\sum}_{i{\gg}n}\;X_i;n{\succeq}1$} satisfies $sup_{k{\succeq}n}{\parallel}T_k{\parallel}=\mathcal{O}p(b_n)$ and ${\frac{sup_{k{\succeq}n}{\parallel}T_k{\parallel}}{B_n}}{\rightarrow\limits^p}0$ for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].
ON THE CONVERGENCE OF SERIES OF MARTINGALE DIFFERENCES WITH MULTIDIMENSIONAL INDICES
Ta Cong Son,Dang Hung Thang 대한수학회 2015 대한수학회지 Vol.52 No.5
Let {Xn; n ≥ 1} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides con- ditions under which the series ∑i≤n Xi converges almost surely and the tail series {Tn = ∑i≫n Xi; n ≥ 1} satisfies supk≥n ∥Tk∥= OP (bn) and supk≥n ∥Tk∥ / Bn P→ 0 for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].
Weak laws of large numbers for weighted coordinatewise pairwise NQD random vectors in Hilbert spaces
Dung Van Le,Son Cong Ta,Cuong Manh Tran 대한수학회 2019 대한수학회지 Vol.56 No.2
In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is $r$ for some $0<r<2$. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.
WEAK LAWS OF LARGE NUMBERS FOR WEIGHTED COORDINATEWISE PAIRWISE NQD RANDOM VECTORS IN HILBERT SPACES
Le, Dung Van,Ta, Son Cong,Tran, Cuong Manh Korean Mathematical Society 2019 대한수학회지 Vol.56 No.2
In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.