Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion un...

We study the functional link between the Hurst parameter and the normalized total wavelet entropy when analyzing fractional Brownian motion (fBm) time series—these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes [L. Zunino, D.G. Pérez, M. Garavaglia, O.A. Rosso, Characterization of laser propagation through turbulent media by...

Fractional Brownian motion with Hurst index less then 1/2 and continuous-time random walk with heavy tailed waiting times (and the corresponding fractional Fokker-Planck equation) are two different processes that lead to a subdiffusive behavior widespread in complex systems. We propose a simple test, based on the analysis of the so-called p variations, which allows distinguishing between the tw...

<p style='text-indent:20px;'>In this paper, we study the existence and uniqueness of mild solutions for neutral delay Hilfer fractional integrodifferential equations with Brownian motion. Sufficient conditions controllability differential motion are established. The required results obtained based on fixed point theorem combined semigroup theory, calculus stochastic analysis. Finally, an ...

Abstract. We study the long-time asymptotics of the probability Pt that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [−L, L] up to time t. We show that for any H ∈]0, 1], for both subdiffusion and superdiffusion regimes, this probability obeys ln(Pt) ∼ −t2H/L2, i.e. may decay slower than exponential (subdiffusion) or faster than expon...