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.
On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes / Abundo, Mario; Pirozzi, Enrica. - In: MATHEMATICS. - ISSN 2227-7390. - 7:10(2019), p. 991. [10.3390/math7100991]
On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes
Pirozzi, Enrica
2019
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.