On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes

Abstract

We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss−Markov process from Doob representation by replacing Brownian motion with fractional Brownian motion. Possible applications in the context of neuronal models are highlighted. A fractional Ornstein−Uhlenbeck process is considered and relations with the integral of the pseudo-fractional Gaussian process are provided.

Keywords

• fractional brownian motion
• gauss–markov process
• fractional ornstein–uhlenbeck