IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i12p2776-2801.html
   My bibliography  Save this article

Approximation of stationary solutions of Gaussian driven stochastic differential equations

Author

Listed:
  • Cohen, Serge
  • Panloup, Fabien

Abstract

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2776-2801
    DOI: 10.1016/j.spa.2011.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911001840
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2011.08.001?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. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    2. Gilles Pag`es & Fabien Panloup, 2007. "Approximation of the distribution of a stationary Markov process with application to option pricing," Papers 0704.0335, arXiv.org, revised Sep 2009.
    3. Crauel, Hans, 1993. "Non-Markovian invariant measures are hyperbolic," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 13-28, March.
    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. 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.
    2. 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.

    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. 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.
    2. Pagès, Gilles & Panloup, Fabien, 2014. "A mixed-step algorithm for the approximation of the stationary regime of a diffusion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 522-565.
    3. Gilles Pagès & Clément Rey, 2023. "Discretization of the Ergodic Functional Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-44, March.
    4. Pagès, Gilles & Rey, Clément, 2020. "Recursive computation of invariant distributions of Feller processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 328-365.
    5. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    6. Panloup, Fabien, 2008. "Computation of the invariant measure for a Lévy driven SDE: Rate of convergence," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1351-1384, August.
    7. Gadat, Sébastien & Panloup, Fabien & Saadane, Sofiane, 2016. "Stochastic Heavy Ball," TSE Working Papers 16-712, Toulouse School of Economics (TSE).
    8. Vincent Lemaire & Thibaut Montes & Gilles Pag`es, 2020. "Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization," Papers 2001.03101, arXiv.org, revised Jul 2020.
    9. Pagès Gilles & Rey Clément, 2019. "Recursive computation of the invariant distributions of Feller processes: Revisited examples and new applications," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 1-36, March.
    10. Chen, Peng & Deng, Chang-Song & Schilling, René L. & Xu, Lihu, 2023. "Approximation of the invariant measure of stable SDEs by an Euler–Maruyama scheme," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 136-167.
    11. Gilles Pagès & Thibaut Montes & Vincent Lemaire, 2020. "Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization," Working Papers hal-02434232, HAL.
    12. Vincent Lemaire & Thibaut Montes & Gilles Pagès, 2022. "Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization," Post-Print hal-02434232, HAL.

    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:121:y:2011:i:12:p:2776-2801. 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.