The purpose of this brief note is to describe a discrete approximation to fractional Brownian motion. The approximation works for all Hurst indices H , but take slightly different forms for H ≤ 1 2 and H > 1 2 . There are already several discrete approximations to fractional Brownian motion in the literature (see, e.g., [11], [1], [3], [10], [4], [2], [5], [8] for this and related topics), and ...

Abstract We study fast/slow systems driven by a fractional Brownian motion B with Hurst parameter $$H\in (\frac{1}{3}, 1]$$ H ∈ ( 1 3 , ] . Surprisingly, the sl...

This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In systems considered, noise correlation function not necessarily related to friction. Thus, there no conventional fluctuation-dissipation relation (FDR) second kind and unique way define a temperature. We start from Markovian process time-dependent diffusivity ...