An analogue for Marcinkiewicz–Zygmund strong law of negatively associated random variables

The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences

“…The main result of this paper fills this gap. Recently, Miao et al [35] have studied the Marcinkiewicz-Zygmund-type strong law of large numbers where the norming constants are of the form n 1/α log β/α n for some β ≥ 0, which is a special case of our result.…”

“…By letting L(x) ≡ 1, Theorem 3.1 generalizes a seminal result of Baum and Katz [1] on complete convergence for sums of independent random variables to weighted sums of negatively associated random variables. Recently, Miao et al [35] proved the following proposition.…”

“…By letting L(x) ≡ 1, Theorem 3.1 generalizes a seminal result of Baum and Katz [1] on complete convergence for sums of independent random variables to weighted sums of negatively associated random variables. Recently, Miao et al [35] proved the following proposition. Proposition 3.2 ([35], Theorem 2.1) Let 0 < α < 2 and let {X, X n , n ≥ 1} be a strictly stationary negatively associated sequence with E|X| α log −β (|X| + 2) < ∞ for some β ≥ 0.…”

The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation

“…where 1 ≤ α < 2, L(x) is a slowly varying function defined on [A, ∞) with some A > 0 and L(x) is the de Bruijn conjugate of L(x). For more conclusions on the M-Z-type strong LLN in the classical framework see Bai and Cheng [21], Chen and Gan [22], Miao, Mu and Xu [23], and Sung [24]. Inspired by Anh et al [20] under the classical framework, in this paper we generalize to the framework of sublinear expectation theory.…”