IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i11p6481-6514.html
   My bibliography  Save this article

An optimal Gauss–Markov approximation for a process with stochastic drift and applications

Author

Listed:
  • Ascione, Giacomo
  • D’Onofrio, Giuseppe
  • Kostal, Lubomir
  • Pirozzi, Enrica

Abstract

We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein–Uhlenbeck type process, by using direct methods of calculus of variations. We show that general power cost functionals satisfy the conditions for existence and uniqueness of the approximation. We provide some examples of general interest and we give bounds on the goodness of the corresponding approximations. Finally, we focus on a model of a neuron embedded in a simple network and we study the approximation of its activity, by exploiting the aforementioned results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6481-6514
    DOI: 10.1016/j.spa.2020.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920302908
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.05.018?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. 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.
    Full references (including those not matched with items on IDEAS)

    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. Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

    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:eee:spapps:v:130:y:2020:i:11:p:6481-6514. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.