We translate into the language of semi-group theory Bismut’s Calculus on boundary processes Bismut 1983 , Lèandre 1989 which gives regularity result on the heat kernel associated with fractional… (More)

This study considers the solution of a class of linear systems related with the fractional Poisson equation FPE −∇2 φ g x, y with nonhomogeneous boundary conditions on a bounded domain. A numerical… (More)

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are… (More)

We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding… (More)

Geometric characteristics of random surfaces play a crucial role in areas such as geoscience, environmetrics, astrophysics, and medical imaging, just to mention a few examples. Numerous real data… (More)

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space R+. Some properties are given and,… (More)

Time-changed Lévy processes include the fractional Poisson process, and the scaling limit of a continuous time random walk. They are obtained by replacing the deterministic time variable by a… (More)

We investigate the properties of multifractal products of the exponential of Ornstein-Uhlenbeck processes driven by Lévy motion. The conditions on the mean, variance and covariance functions of these… (More)

In Chen and Kulik, 2009 , a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis… (More)

We review the application of differential operators of noninteger order to the modeling of dynamic systems. We compare all the definitions of Variable Order VO operators recently proposed in… (More)