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.
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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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Ascione, G., Mishura, Y. & Pirozzi, E. Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications. Methodol Comput Appl Probab 23, 53–84 (2021). https://doi.org/10.1007/s11009-019-09748-y
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DOI: https://doi.org/10.1007/s11009-019-09748-y
Keywords
- Fractional Brownian motion
- Fractional Ornstein-Uhlenbeck process
- Forcing term
- Covariance function
- Asymptotic behavior
- Correlated processes
- Leaky integrate-and-fire neuronal model