In this paper, the complete moment convergence of weighted sums for ρ∗-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for ρ∗-mixing sequence of random...

Let {X <Subscript> n </Subscript>, n ≥ 1} be a sequence of pairwise negatively quadrant dependent (NQD) random variables. In this study, we prove almost sure limit theorems for weighted sums of the random variables. From these results, we obtain a version of the Glivenko–Cantelli lemma for pairwise NQD random...</subscript>

We examine small deviation probabilities of weighted sums of i.i.d.r.v. with a power decay at zero under moment assumptions close to necessary.

Average options are path-dependent and have payoffs which depend on the average price over a fixed period leading up to the maturity date. This option is of interest and important for thinly-traded assets since price manipulation is prohibited, and both the investor and issuer may enjoy a...

In this paper, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are provided. In addition, the Marcinkiewicz-Zygmund type strong law of large...

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the result for many dependent structure, such as END, -mixing, -mixing and -mixing, etc.

In this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sucient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the...