The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of -linearly negative quadrant dependent random variables”.
Pólya processes are natural generalizations of Pólya–Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is a simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤1/2; otherwise, it is called large).
We prove, by means of Malliavin calculus, the convergence in of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters and , when and .
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as