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In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

This paper considers a generalized bidimensional continuous-time risk model with subexponential claims, constant force of interest and Brownian perturbations, where the claim sizes from each line of business are dependent according to some dependence structure and the two components of each claim-inter-arrival-time vector are arbitrarily dependent. Some asymptotic presentations are shown for the finite-time sum ruin probability defined as the probability that the sum of two surplus processes generated by two lines of business goes below zero over a time horizon [ 0 , t ]. Particularly, the claim-number processes from different lines of business can be arbitrarily dependent when the claim sizes are long-tailed and dominatedly-varying-tailed. [ABSTRACT FROM AUTHOR]

In this paper, complete moment convergence for maximum of randomly weighted sums and complete convergence for randomly indexed sums of martingale difference sequences (MDS) are investigated under some proper and sufficient conditions. A Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for MDS is obtained. In addition, relationships among weights, weight functions and boundary functions are revealed in a sense. The results obtained in the paper generalize some corresponding ones for independent and some dependent random variables. As an application, strong consistency for estimators in a nonparametric regression model is established. [ABSTRACT FROM AUTHOR]

In this article, some results on the complete moment convergence for maximal randomly weighted sums of extended negatively dependent (END) random variables are established. In some senses, the results obtained in this article extend the corresponding ones of in reference. As an application of the main results, we consider a result on complete consistency for the weighted estimator in a non parametric regression model based on END errors. We also give a simulation to verify the validity of the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the paper generalize and improve the corresponding ones of Wang et al. (2014b) and Shen, Xue, and Wang (2017). [ABSTRACT FROM AUTHOR]

Abstract.In this article, under some proper and sufficient conditions, we gave complete convergence for weighted sums and maximal weighted sums of arrays of rowwise mn-extended negatively dependent (rowwise mn-END) random variables, which is a new dependent structure. In addition, a relationship between {mn,n≥1} and moment condition for convergence is revealed in a sense. The results obtained in the article generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non parametric regression model is established. [ABSTRACT FROM AUTHOR]

In this article, some results on almost sure convergence for weighted sums of widely negative orthant dependent (WNOD) random variables are presented. The results obtained in the article generalize and improve the corresponding one of J. Lita Da Silva. [(2015), "Almost sure convergence for weighted sums of extended negatively dependent random variables." Acta Math. Hungar. 146 (1), 56-70]. As applications, the strong convergence for the estimator of non parametric regression model are established. [ABSTRACT FROM AUTHOR]