Abstract. In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough path techniques. As a by-product, we provide a natural explanation of the various new asymptotic behaviors in contrast with the classical unweighted ...

Experimental data indicate that stochastic effects exerted at the level of translation contribute substantially to the variation in abundance of proteins expressed at moderate to high levels. This study analyzes the theoretical consequences of fluctuations in residue-specific elongation rates during translation. A simple analytical framework shows that rate variation during elongation gives ris...

Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (X t)t∈T represented as X t = σ(t) ∑ v t α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i.d. standard normal. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of X in terms of compactness properties of (T, d). He...

In this paper, we obtain error bound for pseudo-binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein’s method. We also discuss approximation results independent variables. demonstrate our through some applications in finance runs statistics.

We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I 0 (x) + I 1 (x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due toČekanavičius

We study maximal inequalities for demisubmartingales and N-demisupermartingales and obtain inequalities between dominated demisubmartingales. A sequence of partial sums of zero mean associated random variables is an example of a demimartingale and a sequence of partial sums of zero mean negatively associated random variables is an example of a Ndemimartingale.

The complete moment convergence of weighted sums for arrays of rowwise φ-mixing random variables is investigated. By using moment inequality and truncation method, the sufficient conditions for complete moment convergence of weighted sums for arrays of rowwise φ-mixing random variables are obtained. The results of Ahmed et al. 2002 are complemented. As an application, the complete moment conver...