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

Author

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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)

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.

Suggested Citation

  • Mario Abundo & Enrica Pirozzi, 2019. "On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes," Mathematics, MDPI, vol. 7(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:991-:d:278164
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    References listed on IDEAS

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    1. Mura, A. & Taqqu, M.S. & Mainardi, F., 2008. "Non-Markovian diffusion equations and processes: Analysis and simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064.
    2. Abundo, Mario & Pirozzi, Enrica, 2018. "Integrated stationary Ornstein–Uhlenbeck process, and double integral processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 265-275.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    4. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    Cited by:

    1. Kęstutis Kubilius & Aidas Medžiūnas, 2022. "Pathwise Convergent Approximation for the Fractional SDEs," Mathematics, MDPI, vol. 10(4), pages 1-16, February.
    2. Evgeniya Gospodinova & Penio Lebamovski & Galya Georgieva-Tsaneva & Galina Bogdanova & Diana Dimitrova, 2022. "Methods for Mathematical Analysis of Simulated and Real Fractal Processes with Application in Cardiology," Mathematics, MDPI, vol. 10(19), pages 1-16, September.

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