IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i5d10.1007_s00362-025-01742-6.html
   My bibliography  Save this article

Nonparametric estimation for distribution dependent SDEs driven by fractional brownian motions with random effects

Author

Listed:
  • Guangjun Shen

    (Anhui Normal University)

  • Qian Yu

    (Nanjing University of Aeronautics and Astronautics)

  • Huan Zhou

    (Anhui Normal University)

Abstract

In this paper, we study a nonparametric estimation of random effects from the following distribution dependent SDE driven by fractional Brownian motions $$\begin{aligned} dX^j_t=\beta _jb(t,X^j_t,\mathcal {L}_{X_t^j})dt+\varepsilon \sigma (t, \mathcal {L}_{X^j_t})dB_t^{j,H}, ~X^j_0=x^j_0, ~0\le t\le T, \end{aligned}$$ where $$j=1,2,\cdots,N$$ , $$\mathcal {L}_{X^j_t}$$ denotes the law of $$X^j_t$$ , $$B_t^{1, H},\cdots,B_t^{N, H}$$ are independent fractional Brownian motions with common Hurst parameter $$H\in (1/2,1)$$ and $$\beta _j$$ is random variable independent of $$B^{j,H}$$ . This result extends the existing results of non parametric estimation to the case of distribution dependent. Moreover, we consider the estimation for the density function of $$\beta _j$$ under weaker conditions of kernel function and study the corresponding asymptotic distribution.

Suggested Citation

  • Guangjun Shen & Qian Yu & Huan Zhou, 2025. "Nonparametric estimation for distribution dependent SDEs driven by fractional brownian motions with random effects," Statistical Papers, Springer, vol. 66(5), pages 1-22, August.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01742-6
    DOI: 10.1007/s00362-025-01742-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01742-6
    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/s00362-025-01742-6?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01742-6. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.