In the paper, the complete moment convergence is obtained for i.i.d. random variables such that all moments exist, but the moment generating function does not exist. The main results extend the related known works due to Gut and Stadtmüller.

In this work, a sharp upper bound on the law of the logarithm for the weighted sums of random variables with multidimensional indices is obtained. The main result improves the result in [Li, Rao and Wang, 1995. On strong law of large numbers and the law of the logarithm for weighted sums of...

Let {Yi,-[infinity]i[infinity]} be a doubly infinite sequence of identically distributed [phi]-mixing random variables, {ai,-[infinity]i[infinity]} be an absolutely summable sequence of real numbers. In this paper we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large...

In this paper, we obtain the Hajeck-Rényi inequality and discuss the Marcinkiewicz strong law of large numbers for negatively associated random variables. In particular, the classical Marcinkiewicz strong law of large numbers for independent and identically distributed random variables is...

Let {Xn,n>=1} be a sequence of identically distributed [rho]-mixing random variables and set . Under suitable mixing rate restriction, the sufficient and necessary conditions for the existence of the moments of supn>=1Sn/n1/rp(0<r<2,p>0) are given, which are same as that in the independent case.

This paper obtains the Embrechts-Veraverbeke asymptotic formula for the random walk with dependent steps, where the steps constitute a sequence of negatively associated random variables with a common heavy-tailed distribution such that its left tail is lighter than its right tail.

In the paper, the upper bound and lower bound of the law of the single logarithm (LSL) are established under the condition that the sequence of the normalized weighted sums of random elements is bounded in probability. The main result improves the upper bound in [Sung, S.H., 2009. A law of the...

Let {an,n≥1} be a sequence of positive constants with an/n↑ and let {X,Xn,n≥1} be a sequence of pairwise independent identically distributed random variables. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X,Xn,n≥1}, which are...