Rosenthal Inequality for NOD Sequences and Its Applications

Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.

GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

Inequalities of Maximum of Partial Sums and Convergence Rates in the Strong Laws for ρ^-mixing Random Variables

In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.

CONVERGENCE RATES IN THE STRONG LAWS FOR A CLASS OF DEPENDENT RANDOM FIELDS

By using a Rosenthal type inequality established in this paper,the complete convergence rates in the strong laws for a class of dependent random fields are discussed.And the result obtained extends those for ρ --mixing random fields,ρ *-mixing random fields and negatively associated fields.

On a Version of Rosenthal’s Inequality for Locally Square Integrable Martingales

In this paper, we study the constants in a version of Rosenthal’s inequality for locally square integrable martingales. We prove that the order of growth rates of the constants is the same as in the case of discrete time martingales.

Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications

In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.

Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.

Rosenthal type inequalities for B-valued strong mixing random fields and their applications

Some inequalities for moments of partial sums of a B valued strong mixing field are established and their applications to the weak and strong laws of large numbers and the complete convergences are discussed.

Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables

In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^＊ -mixing random fields,

Moment inequalities for the partial sums of random variables

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.

L_(p,q)-norm estimates associated with Burkholder’s inequalities

We prove Burkholder's inequalities in the frame of Lorentz spaces Lp,q(Ω), 1 < p < ∞, 1 < q < ∞. As application, we obtain the Lp,q-norm estimates on Rosenthal's inequalities. These estimates generalize the classical Rosenthal's inequalities.