IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i1d10.1007_s11009-019-09748-y.html
   My bibliography  Save this article

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

Author

Listed:
  • Giacomo Ascione

    (Università di Napoli FEDERICO II)

  • Yuliya Mishura

    (Taras Shevchenko National University of Kyiv)

  • Enrica Pirozzi

    (Università di Napoli FEDERICO II)

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.

Suggested Citation

  • Giacomo Ascione & Yuliya Mishura & Enrica Pirozzi, 2021. "Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 53-84, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-019-09748-y
    DOI: 10.1007/s11009-019-09748-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09748-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-019-09748-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Cohen, Serge & Panloup, Fabien, 2011. "Approximation of stationary solutions of Gaussian driven stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2776-2801.
    3. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
    4. Herold Dehling & Brice Franke & Jeannette H. C. Woerner, 2017. "Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 1-14, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    2. Solesne Bourguin & Thanh Dang & Konstantinos Spiliopoulos, 2023. "Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-57, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Selim Amrouni & Aymeric Moulin & Tucker Balch, 2022. "CTMSTOU driven markets: simulated environment for regime-awareness in trading policies," Papers 2202.00941, arXiv.org, revised Feb 2022.
    2. Qian Yu, 2021. "Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean for general Hurst parameter," Statistical Papers, Springer, vol. 62(2), pages 795-815, April.
    3. 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.
    4. 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.
    5. Lefebvre, Mario, 2024. "Exact solution to a first-passage problem for an Ornstein–Uhlenbeck process with jumps and its integral," Statistics & Probability Letters, Elsevier, vol. 205(C).
    6. Ascione, Giacomo & D’Onofrio, Giuseppe & Kostal, Lubomir & Pirozzi, Enrica, 2020. "An optimal Gauss–Markov approximation for a process with stochastic drift and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6481-6514.
    7. Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    8. Reinhard Höpfner, 2021. "Polynomials under Ornstein–Uhlenbeck noise and an application to inference in stochastic Hodgkin–Huxley systems," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 35-59, April.
    9. He, Yue & Kawai, Reiichiro, 2022. "Super- and subdiffusive positions in fractional Klein–Kramers equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    10. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    11. Giuseppe D’Onofrio & Claudio Macci & Enrica Pirozzi, 2018. "Asymptotic Results for First-Passage Times of Some Exponential Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1453-1476, December.
    12. Radomyra Shevchenko & Ciprian A. Tudor, 2020. "Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 227-247, April.
    13. Cohen, Serge & Panloup, Fabien & Tindel, Samy, 2014. "Approximation of stationary solutions to SDEs driven by multiplicative fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1197-1225.
    14. Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-019-09748-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.