Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of...

In this paper, some probability inequalities and moment inequalities for widely orthant-dependent (WOD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality. By using these inequalities, we further study the complete...

We extend the Brunk-Prokhorov strong law of large numbers and obtain a strong growth rate for martingale differences. Some results for demimartingales are also given.

In this paper, we investigate Marshall type inequalities for demimartingales and as a further study, we obtain minimal Marshall type inequalities for nonnegative demimartingales. In addition, the convex function type inequalities for demimartingales and N-demimartingales are presented. Our...

In this paper, we establish some maximal inequalities for N-demimartingale. The maximal inequality for N-demimartingale is used as a key inequality to establish other results including the strong law of large numbers, strong growth rate and the integrability of supremum for N-demimartingale.

A Hjek-Rnyi-type inequality for associated random variables was obtained by Prakasa Rao [Prakasa Rao, B.L.S., 2002. Hjek-Rnyi-type inequality for associated sequences. Statist. Probab. Lett. 57, 139-143]. Recently, Sung [Sung, H.S., 2008. A note on the Hjek-Rnyi inequality for associated random...

A new extension of the Borel-Cantelli Lemma was obtained by Xie [Xie, Y.Q., 2008. A bilateral inequality on the Borel-Cantelli Lemma. Statist. Probab. Lett. 78, 2052-2057], and an important bilateral inequality on the Borel-Cantelli Lemma was given. However, there are several mistakes in the...

<Para ID="Par1">In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of...</para>