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

Mario Abundo and Enrica Pirozzi
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Mario Abundo: Dipartimento di Matematica, Università “Tor Vergata”, 00133 Rome, Italy
Enrica Pirozzi: Dipartimento di Matematica e Applicazioni, Università “Federico II”, Complesso Monte S. Angelo, 80126 Napoli, Italy

Mathematics, 2019, vol. 7, issue 10, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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