IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i10p3102-3123.html
   My bibliography  Save this article

Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations

Author

Listed:
  • Mei, Hongwei
  • Yin, George
  • Wu, Fuke

Abstract

This work focuses on properties of stochastic integro-differential equations with infinite delay (or unbounded delay). Our main approach is to map the solution processes into another Polish space. Under suitable conditions, it is shown that the resulting processes are Markov. Furthermore, sufficient conditions for Feller properties, recurrence, ergodicity, and existence of invariant measures are obtained. Moreover, weak sense Fokker–Planck equations are derived for the underlying processes.

Suggested Citation

  • Mei, Hongwei & Yin, George & Wu, Fuke, 2016. "Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3102-3123.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3102-3123
    DOI: 10.1016/j.spa.2016.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916300254
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.04.003?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. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
    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. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(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. Fawaz E. Alsaadi & Lichao Feng & Madini O. Alassafi & Reem M. Alotaibi & Adil M. Ahmad & Jinde Cao, 2022. "Stochastic Robustness of Delayed Discrete Noises for Delay Differential Equations," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    2. Wang, Zhen & Li, Xiong & Lei, Jinzhi, 2014. "Moment boundedness of linear stochastic delay differential equations with distributed delay," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 586-612.
    3. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    4. Zhou, Shaobo & Hu, Yangzi, 2016. "Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 126-138.
    5. Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).

    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:126:y:2016:i:10:p:3102-3123. 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.