In this article, we study the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables under sub-linear expectations. We also give some sufficient assumptions for the convergence. Moreover, we get the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables. The results obtained in this paper generalize the relevant ones in probability space.

In this paper, the complete moment convergence for the maximal partial sums of moving average processes generated by $\{Y_i,-\mathrm{\infty }<i<\mathrm{\infty }\}$ is proved under conditions that $C_{\mathbb{V}}\left(|Y_1{|}^p\left(1\vee l(f^{-1}(Y_1))\right)\right)<\mathrm{\infty }$, where $f^{-1}$ is the inverse function of $f$, and $\{Y_i,-\mathrm{\infty }<i<\mathrm{\infty }\}$ is a double sequence of identically distributed, negatively dependent random variables under sublinear expectations. The results established in sublinear expectation spaces complement and extend the corresponding ones in probability space in some extent.

In this article, the complete moment convergence for the partial sum of moving average processes $\{X_n=\sum _{i=-\mathrm{\infty }}^{\mathrm{\infty }}{a}_i{Y}_{i+n},n\ge 1\}$ is established under some proper conditions, where $\{Y_i,-\mathrm{\infty }<i<\mathrm{\infty }\}$ is a sequence of $m$-widely acceptable ( $m$-WA) random variables, which is stochastically dominated by a random variable $Y$ in sub-linear expectations space $(\mathrm{\Omega },\mathcal{H},\mathbb{E})$, and $\{a_i,-\mathrm{\infty }<i<\mathrm{\infty }\}$ is an absolutely summable sequence of real numbers. The results extend the relevant results in probability space to those under sub-linear expectations. A Rosenthal-type inequality for $m$-WA random variables is also eatablished.

In this article, we study the complete convergence and the complete moment convergence for negatively dependent (ND) random variables under sub-linear expectations. Under proper conditions of the moment of random variables, we establish the complete convergence and the complete moment convergence. As applications, we obtain the Marcinkiewcz-Zygmund type strong law of large numbers of ND random variables under sub-linear expectations. The results here generalize the corresponding ones in classic probability space to those under sub-linear expectations.

In this article, we study complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations. The results obtained in sub-linear expectation spaces extend the corresponding ones in probability space.