IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i11p1805-1818.html
   My bibliography  Save this article

Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

Author

Listed:
  • Zhang, Xicheng

Abstract

In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.

Suggested Citation

  • Zhang, Xicheng, 2005. "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1805-1818, November.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:11:p:1805-1818
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00079-7
    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. Dejun Luo, 2015. "Quasi-invariance of the Stochastic Flow Associated to Itô’s SDE with Singular Time-Dependent Drift," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1743-1762, December.
    2. Jinxia Wang, 2015. "Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients," Journal of Mathematics, Hindawi, vol. 2015, pages 1-5, May.
    3. Xia, Pengcheng & Xie, Longjie & Zhang, Xicheng & Zhao, Guohuan, 2020. "Lq(Lp)-theory of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5188-5211.
    4. G. Prato & F. Flandoli & E. Priola & M. Röckner, 2015. "Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1571-1600, December.
    5. Xie, Longjie, 2017. "Singular SDEs with critical non-local and non-symmetric Lévy type generator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3792-3824.
    6. Holden, Helge & Karlsen, Kenneth H. & Pang, Peter H.C., 2022. "Strong solutions of a stochastic differential equation with irregular random drift," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 655-677.
    7. Krylov, N.V., 2021. "On stochastic Itô processes with drift in Ld," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 1-25.
    8. Luo, Dejun, 2011. "Absolute continuity under flows generated by SDE with measurable drift coefficients," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2393-2415, October.
    9. Wujun Lv & Xing Huang, 2021. "Harnack and Shift Harnack Inequalities for Degenerate (Functional) Stochastic Partial Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 34(2), pages 827-851, June.
    10. Yang, Saisai & Zhang, Tusheng, 2023. "Strong solutions to reflecting stochastic differential equations with singular drift," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 126-155.

    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:115:y:2005:i:11:p:1805-1818. 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.