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Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications

  • Giacomo AscioneEmail author
  • Yuliya Mishura
  • Enrica Pirozzi
Article
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Abstract

We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing process. Applications of this process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this process are given.

Keywords

Fractional Brownian motion Fractional Ornstein-Uhlenbeck process Forcing term Covariance function Asymptotic behavior Correlated processes Leaky integrate-and-fire neuronal model 

Mathematics Subject Classification (2010)

60G22 60G15 68U20 

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Notes

Acknowledgments

We would like to thank anonymous Reviewers and also Editor for their useful comments. The research of Yu. Mishura was carried through within the frame and support of the ToppForsk project nr. 274410 of the Research Council of Norway with title STORM: Stochastics for Time-Space Risk Models. This research was also partially funded by GNCS. This research is partially supported by MIUR - PRIN 2017, project ”Stochastic Models for Complex Systems”, no. 2017JFFHSH.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Napoli FEDERICO IINapoliItaly
  2. 2.Department of Probability Theory, Statistics and Actuarial MathematicsTaras Shevchenko National University of KyivKyivUkraine

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