IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v129y2017icp222-229.html
   My bibliography  Save this article

Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion

Author

Listed:
  • Boufoussi, Brahim
  • Hajji, Salah

Abstract

In this paper, we prove an existence and uniqueness result of mild solution for a stochastic delay differential equation in a Hilbert space driven by a fractional Brownian motion with the Hurst parameter H>1∕2 and with a non-deterministic diffusion coefficient. We also prove under a sufficient condition that the law of the norm of the solution admits a density with respect to Lebesgue measure on R.

Suggested Citation

  • Boufoussi, Brahim & Hajji, Salah, 2017. "Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 222-229.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:222-229
    DOI: 10.1016/j.spl.2017.06.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217302109
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.06.006?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. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    2. Grecksch, W. & Anh, V. V., 1999. "A parabolic stochastic differential equation with fractional Brownian motion input," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 337-346, February.
    3. Duncan, T.E. & Maslowski, B. & Pasik-Duncan, B., 2005. "Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise," Stochastic Processes and their Applications, Elsevier, vol. 115(8), pages 1357-1383, August.
    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. Xu, Xiao & Wang, Li & Du, Zhenbin & Kao, Yonggui, 2023. "H∞ Sampled-Data Control for Uncertain Fuzzy Systems under Markovian Jump and FBm," Applied Mathematics and Computation, Elsevier, vol. 451(C).

    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. Issoglio, E. & Riedle, M., 2014. "Cylindrical fractional Brownian motion in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3507-3534.
    2. Zhang, Yinghan & Yang, Xiaoyuan, 2015. "Fractional stochastic Volterra equation perturbed by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 20-36.
    3. Fan, Xiliang & Yuan, Chenggui, 2016. "Lyapunov exponents of PDEs driven by fractional noise with Markovian switching," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 39-50.
    4. Barbu, Viorel & Brzeźniak, Zdzisław & Hausenblas, Erika & Tubaro, Luciano, 2013. "Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 934-951.
    5. Lihong Guo, 2024. "Renormalization Group Method for a Stochastic Differential Equation with Multiplicative Fractional White Noise," Mathematics, MDPI, vol. 12(3), pages 1-20, January.
    6. Duncan, T.E. & Maslowski, B. & Pasik-Duncan, B., 2005. "Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise," Stochastic Processes and their Applications, Elsevier, vol. 115(8), pages 1357-1383, August.
    7. Čoupek, P. & Maslowski, B., 2017. "Stochastic evolution equations with Volterra noise," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 877-900.
    8. Nguyen Tien, Dung, 2013. "The existence of a positive solution for a generalized delay logistic equation with multifractional noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1240-1246.
    9. Gao, Fengyin & Kang, Yanmei, 2021. "Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Ren, Yong & Hou, Tingting & Sakthivel, R. & Cheng, Xing, 2014. "A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 658-665.
    11. Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    12. Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
    13. Zhi Li & Litan Yan, 2019. "Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1399-1419, September.

    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:stapro:v:129:y:2017:i:c:p:222-229. 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/622892/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.