Fourier (spectral) transform and multivariate temporal dynamics. The Fourier transform has
become a universal tool in almost all fields of the sciences. Notably, it has been used to …

Empirical studies have shown that traffic in communication networks exhibits long-range
dependence. Cumulative network traffic is often thought to be well modelled by a fractional …

This article considers multivariate linear processes whose components are either short-or
long-range dependent. The functional central limit theorems for the sample mean and the …

Fractional Brownian motion approximation of queueing networks has been studied
extensively. In the existing results related to this topic, the Hurst parameter of …

Operator self-similar processes, as an extension of self-similar processes, have been
studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors …

This article considers multivariate linear processes whose components are either short-or
long-range dependent. The functional central limit theorems for the sample mean and the …

We study the problem of the approximation in law of the Rosenblatt sheet. We prove the
convergence in law of two families of process to the Rosenblatt sheet: the first one is …

It is well known that martingale difference sequences are very useful in applications and
theory. On the other hand, the operator fractional Brownian motion as an extension of the …

This thesis is concerned with high-dimensional time series in the context of long-range
dependence and nonstationarity. It is composed of three major parts. The first two parts …

In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we
introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some …