Gaussian processes that are multifractional are studied in this paper. By multifractional processes we mean that they behave locally like a fractional Brownian motion, but the fractional index is no more a constant: it is a function. We introduce estimators of this multifractional function based...

In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener...

In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a...

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific...

Self-similar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields,...