In this article, further properties of the Riesz-Bessel distribution are provided. These properties allow for the simulation of random variables from the Riesz-Bessel distribution. Estimation is addressed by nonlinear generalized least squares regression on the empirical characteristic function....

Soft Computing admits approximate reasoning, imprecision, uncertainty and partial truth in order to mimic aspects of the remarkable human capability of making decisions in real-life and ambiguous environments. "Soft Computing in Industrial Applications" contains a collection of papers that were...

This paper presents the log-normal, log-gamma and log-negative inverted gamma scenarios in limit theorems for multifractal products of stochastic processes with long-range dependence.

This paper presents a class of minimum contrast estimators for stochastic processes with possible long-range dependence based on the information on higher-order spectral densities. The results on consistency and asymptotic normality of the proposed estimators are provided.

The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of...

In this paper, we examine the finite-sample properties of the approximate maximum likelihood estimate (MLE) of the fractional differencing parameter d in an ARFIMA(p, d, q) model based on the wavelet coefficients. Ignoring wavelet coefficients of higher order of resolution, the remaining wavelet...

Fractional Brownian motion (fBm) is fundamental in studying the phenomenon of long-range dependence in a wide range of fields. However, since fBm is not a semimartingale, some restrictions have been imposed on an fBm stochastic calculus. This paper studies fractional Riesz-Bessel motion (fRBm),...

A class of stochastic fractional-order differential models with homogeneous boundary conditions on a fractal set is introduced. The corresponding solution class satisfies a weak-sense Markov condition with respect to domains with fractal boundary. Some examples are given which provide a...