IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v148y2019icp118-127.html
   My bibliography  Save this article

Stochastic flows of SDEs with non-Lipschitz coefficients and singular time

Author

Listed:
  • Xu, Jie
  • Wen, Jiaping
  • Mu, Jianyong
  • Liu, Jicheng

Abstract

In this paper we prove the stochastic homeomorphism flows for stochastic differential equations (SDEs) with non-Lipschitz coefficients and singular time.

Suggested Citation

  • Xu, Jie & Wen, Jiaping & Mu, Jianyong & Liu, Jicheng, 2019. "Stochastic flows of SDEs with non-Lipschitz coefficients and singular time," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 118-127.
  • Handle: RePEc:eee:stapro:v:148:y:2019:i:c:p:118-127
    DOI: 10.1016/j.spl.2019.01.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521930032X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2019.01.026?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. Zhang, Xicheng, 2010. "Stochastic flows and Bismut formulas for stochastic Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1929-1949, September.
    2. Lan, Guangqiang & Wu, Jiang-Lun, 2014. "New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4030-4049.
    3. Qiao, Huijie & Zhang, Xicheng, 2008. "Homeomorphism flows for non-Lipschitz stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2254-2268, December.
    4. Zhang, Xicheng, 2005. "Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 435-448, March.
    Full references (including those not matched with items on IDEAS)

    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. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta Hedging in a Jump-Diffusion Model," Papers 1910.08946, arXiv.org, revised Apr 2022.
    2. Qiao, Huijie & Zhang, Xicheng, 2008. "Homeomorphism flows for non-Lipschitz stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2254-2268, December.
    3. Qiao, Huijie & Zhang, Xicheng, 2007. "Homeomorphism of solutions to backward SDEs and applications," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 399-408, March.
    4. 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.
    5. Zhang, Xicheng, 2010. "Stochastic flows and Bismut formulas for stochastic Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1929-1949, September.
    6. Junxia Duan & Jun Peng, 2022. "An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients," Journal of Theoretical Probability, Springer, vol. 35(1), pages 575-602, March.
    7. Luo, Dejun, 2008. "Isotropic stochastic flow of homeomorphisms on associated with the critical Sobolev exponent," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1463-1488, August.
    8. Feng-Yu Wang, 2014. "Derivative Formula and Gradient Estimates for Gruschin Type Semigroups," Journal of Theoretical Probability, Springer, vol. 27(1), pages 80-95, March.
    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. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.
    11. Uda, Kenneth, 2021. "Averaging principle for stochastic differential equations in the random periodic regime," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 1-36.
    12. 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.
    13. Lan, Guangqiang & Xia, Fang & Zhao, Mei, 2020. "pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 160(C).
    14. Jianhai Bao & Xing Huang & Chenggui Yuan, 2019. "Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts," Journal of Theoretical Probability, Springer, vol. 32(2), pages 848-871, June.
    15. Bao, Jianhai & Wang, Feng-Yu & Yuan, Chenggui, 2019. "Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4576-4596.
    16. Zhang, Xicheng, 2013. "Derivative formulas and gradient estimates for SDEs driven by α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1213-1228.
    17. Wu, Bo & Wu, Jiang-Lun, 2018. "Characterising the path-independent property of the Girsanov density for degenerated stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 71-79.
    18. Yan, Litan & Yin, Xiuwei, 2018. "Bismut formula for a stochastic heat equation with fractional noise," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 165-172.

    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:148:y:2019:i:c:p:118-127. 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.