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...

Non-Gaussian limiting distributions of the rescaling solutions of the heat equation for non-Gaussian initial data with long-range dependence are discribed in terms of their multiple stochastic integral representations.

Gaussian and non-Gaussian limiting distributions of the rescaled solutions of the fractional (in time) diffusion-wave equation for Gaussian and non-Gaussian initial data with long-range dependence are described in terms of multiple Wiener-Itô integrals.

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...

An existence and uniqueness theorem is proved for a quasilinear stochastic evolution equation with an additive noise in the form of a stochastic integral with respect to a Hilbert space-valued fractional Borwnian motion. Ideas of the finite-dimensional approximation by the Galerkin method are used.

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...

A fractional version of the heat equation, involving fractional powers of the negative Laplacian operator, with random initial conditions of exponential type, is introduced. Two cases are considered, depending on whether the Hopf-Cole transformation of such random initial conditions coincides,...