IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v72y1997i1p73-95.html
   My bibliography  Save this article

Anticipating stochastic Volterra equations

Author

Listed:
  • Alòs, Elisa
  • Nualart, David

Abstract

In this paper we establish the existence and uniqueness of a solution for stochastic Volterra equations assuming that the coefficients F(t,s,x) and Gi(t,s,x) are Ft-measurable, for s[less-than-or-equals, slant]t, where {Ft} denotes the filtration generated by the driving Brownian motion. We impose some differentiability assumptions on the coefficients, in the sense of the Malliavin calculus, in the time interval [s,t]. Some properties of the solution are discussed.

Suggested Citation

  • Alòs, Elisa & Nualart, David, 1997. "Anticipating stochastic Volterra equations," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 73-95, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:73-95
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00075-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Deya, Aurélien & Tindel, Samy, 2011. "Rough Volterra equations 2: Convolutional generalized integrals," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1864-1899, August.
    2. David J. Promel & David Scheffels, 2022. "Pathwise uniqueness for singular stochastic Volterra equations with H\"older coefficients," Papers 2212.08029, arXiv.org, revised Jul 2024.
    3. Aur'elien Alfonsi & Guillaume Szulda, 2024. "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients," Papers 2402.19203, arXiv.org, revised Jul 2024.
    4. Jie, Lijuan & Luo, Liangqing & Zhang, Hua, 2024. "One-dimensional McKean–Vlasov stochastic Volterra equations with Hölder diffusion coefficients," Statistics & Probability Letters, Elsevier, vol. 205(C).
    5. Prömel, David J. & Scheffels, David, 2023. "Stochastic Volterra equations with Hölder diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 291-315.
    6. Herv'e Andr`es & Benjamin Jourdain, 2024. "Existence, uniqueness and positivity of solutions to the Guyon-Lekeufack path-dependent volatility model with general kernels," Papers 2408.02477, arXiv.org.

    More about this item

    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:eee:spapps:v:72:y:1997:i:1:p:73-95. 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: 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.