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On the complete convergence for sequences of dependent random variables via stochastic domination conditions and regularly varying functions theory
Nguyen Chi Dzung, Lê Vǎn Thành
This note develops Rio's proof [C. R. Math. Acad. Sci. Paris, 1995] of the rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers to the case of sums of depe…
On the Baum--Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants
Lê Vǎn Thành
This paper proves the Baum--Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditio…
The Marcinkiewicz--Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences
Vu Thi Ngoc Anh, Nguyen Thi Thanh Hien, Lê Vǎn Thành +1
This paper establishes complete convergence for weighted sums and the Marcinkiewicz--Zygmund-type strong law of large numbers for sequences of negatively associated and identically…
On Complete Convergence in Mean for Double Sums of Independent Random Elements in Banach Spaces
Le Van Thanh, Nguyen Thi Thuy
In this work, conditions are provided under which a normed double sum of independent random elements in a real separable Rademacher type Banach space converges completely to $0…