Since the 60s of last century Fractional Calculus exhibited a remarkable progress and
presently it is recognized to be an important topic in the scientific arena. This survey …

Fractional Calculus (FC) was a bright idea of Gottfried Leibniz originating in the end of the
seventeenth century. The topic was developed mainly in a mathematical framework, but …

Abstract The well-known Ornstein–Uhlenbeck process (OUP) is the central go-to Gaussian
model for statistical-equilibrium processes. The recently-introduced power Brownian motion …

Many results in the theory of Gaussian processes rely on the eigenstructure of the
covariance operator. However, eigenproblems are notoriously hard to solve explicitly and …

In this work, the continuity with respect to the Hurst parameter of solutions to stochastic
evolution equations is studied. Compared with recent studies on such continuity property …

Let BH be a fractional Brownian motion with Hurst index 1 2≤ H< 1. In this paper, we
consider the linear self-attracting diffusion X t H= B t H-θ∫ 0 t∫ 0 s X s HX u H duds+ ν t with …

The problem of investigating the continuity in the Hurst index arises naturally in statistical
inferences related to fractional Brownian motion. In this paper, based on the techniques of …

This is a guide to the mathematical theory of Brownian motion and related stochastic
processes, with indications of how this theory is related to other branches of mathematics …

This paper contributes in three stages in a logic of the cognitive process: we firstly propose a
new estimation of Hurst exponent by changing frequency method which is purely …

We study statistical inference for small-noise-perturbed multiscale dynamical systems where
the slow motion is driven by fractional Brownian motion. We develop statistical estimators for …