IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i11-12p962-968.html
   My bibliography  Save this article

Finite and infinite time interval BSDEs with non-Lipschitz coefficients

Author

Listed:
  • Fan, ShengJun
  • Jiang, Long

Abstract

This paper aims at solving multidimensional backward stochastic differential equations (BSDEs) under weaker assumptions on the coefficients, considering both a finite and an infinite time interval. We establish a general existence and uniqueness result of the solutions to finite and infinite time interval BSDEs with non-Lipschitz coefficients, which generalizes the corresponding results in Mao (1995), Wang and Wang (2003), Wang and Huang (2009), Chen (1997) and Chen and Wang (2000).

Suggested Citation

  • Fan, ShengJun & Jiang, Long, 2010. "Finite and infinite time interval BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 962-968, June.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:11-12:p:962-968
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00049-0
    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.

    References listed on IDEAS

    as
    1. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    2. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    3. Wang, Ying & Huang, Zhen, 2009. "Backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1438-1443, June.
    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. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Tie Wang & Siyu Cui, 2022. "Anticipated Backward Doubly Stochastic Differential Equations with Non-Lipschitz Coefficients," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    3. Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(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. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(C).
    3. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    4. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    5. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    6. Liu, Jicheng & Ren, Jiagang, 2002. "Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 93-100, January.
    7. Wu, Hao & Wang, Wenyuan & Ren, Jie, 2012. "Anticipated backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 672-682.
    8. Yu, Xianye, 2019. "Non-Lipschitz anticipated backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    9. Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
    10. Sheng-Jun Fan & Long Jiang, 2012. "A Generalized Comparison Theorem for BSDEs and Its Applications," Journal of Theoretical Probability, Springer, vol. 25(1), pages 50-61, March.
    11. Wang, Ying & Huang, Zhen, 2009. "Backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1438-1443, June.
    12. Cody B. Hyndman & Polynice Oyono Ngou, 2017. "A Convolution Method for Numerical Solution of Backward Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 1-29, March.
    13. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    14. Fan, Shengjun & Hu, Ying & Tang, Shanjian, 2023. "Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 335-375.
    15. Xiong, Yafang & Xu, Xiaoming, 2020. "Anticipated backward stochastic differential equations with left-Lipschitz coefficient," Statistics & Probability Letters, Elsevier, vol. 163(C).
    16. Qin, Yan & Xia, Ning-Mao, 2013. "Variational approach for the adapted solution of the general backward stochastic differential equations under the Bihari condition," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1271-1281.
    17. Fan, ShengJun & Liu, DeQun, 2010. "A class of BSDE with integrable parameters," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2024-2031, December.
    18. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    19. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    20. Possamaï, Dylan, 2013. "Second order backward stochastic differential equations under a monotonicity condition," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1521-1545.

    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:80:y:2010:i:11-12:p:962-968. 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.