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Open AccessArticle

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

1
Dipartimento di Matematica, Università “Tor Vergata”, 00133 Rome, Italy
2
Dipartimento di Matematica e Applicazioni, Università “Federico II”, Complesso Monte S. Angelo, 80126 Napoli, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(10), 991; https://doi.org/10.3390/math7100991
Received: 28 June 2019 / Revised: 28 September 2019 / Accepted: 16 October 2019 / Published: 18 October 2019
(This article belongs to the Special Issue Stochastic Processes in Neuronal Modeling)
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. View Full-Text
Keywords: fractional Brownian motion; Gauss–Markov process; fractional Ornstein–Uhlenbeck fractional Brownian motion; Gauss–Markov process; fractional Ornstein–Uhlenbeck
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Abundo, M.; Pirozzi, E. On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes. Mathematics 2019, 7, 991.

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