Convergence for sums of i.i.d. random variables under sublinear expectations

In this paper, we obtain equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent identically distributed random variables under sublinear expectations space. The results obtained in the paper are extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space.

Convergence Theorems for m -Coordinatewise Negatively Associated Random Vectors in Hilbert Spaces

In this study, some new results on convergence properties for m -coordinatewise negatively associated random vectors in Hilbert space are investigated. The weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for linear process of H-valued m -coordinatewise negatively associated random vectors with random coefficients are established. These results improve and generalise some corresponding ones in the literature.

Complete moment convergence of moving average processes for m-WOD sequence

In this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

Complete integration convergence for arrays of rowwise extended negatively dependent random variables under the sub-linear expectations

<abstract><p>Limit theorems of sub-linear expectations are challenging field that has attracted widespread attention in recent years. In this paper, we establish some results on complete integration convergence for weighted sums of arrays of rowwise extended negatively dependent random variables under sub-linear expectations. Our results generalize the complete moment convergence of the probability space to the sub-linear expectation space.</p></abstract>

Complete convergence and complete moment convergence for arrays of Rowwise asymptotically almost negatively associated random variables under the sub-linear expectations

In this article, we investigate the complete convergence and complete moment convergence for maximal partial sums of asymptotically almost negatively associated random variables under the sublinear expectations. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.