IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v198y2023ics016771522300072x.html
   My bibliography  Save this article

A deviation inequality for increment of a G-Brownian motion under G-expectation and applications

Author

Listed:
  • Xu, Jie

Abstract

In this paper, we prove a deviation inequality for increments of a G-Brownian motion under G-expectation. As an application, we obtain a functional modulus of continuity for a G-Brownian motion.

Suggested Citation

  • Xu, Jie, 2023. "A deviation inequality for increment of a G-Brownian motion under G-expectation and applications," Statistics & Probability Letters, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:stapro:v:198:y:2023:i:c:s016771522300072x
    DOI: 10.1016/j.spl.2023.109848
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522300072X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109848?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. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    2. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    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. Hu, Mingshang & Wang, Falei & Zheng, Guoqiang, 2016. "Quasi-continuous random variables and processes under the G-expectation framework," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2367-2387.
    2. Hu, Mingshang & Ji, Xiaojun & Liu, Guomin, 2021. "On the strong Markov property for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 417-453.
    3. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    4. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    5. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    6. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    7. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    8. Li, Hanwu & Peng, Shige, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
    9. Criens, David & Niemann, Lars, 2024. "A class of multidimensional nonlinear diffusions with the Feller property," Statistics & Probability Letters, Elsevier, vol. 208(C).
    10. 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).
    11. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    12. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    13. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    14. Denk, Robert & Kupper, Michael & Nendel, Max, 2020. "A semigroup approach to nonlinear Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1616-1642.
    15. Lin, Qian, 2019. "Jensen inequality for superlinear expectations," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 79-83.
    16. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    17. Peng Luo & Falei Wang, 2019. "Viability for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(1), pages 395-416, March.
    18. Nendel, Max, 2019. "On Nonlinear Expectations and Markov Chains under Model Uncertainty," Center for Mathematical Economics Working Papers 628, Center for Mathematical Economics, Bielefeld University.
    19. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    20. Shige Peng & Shuzhen Yang & Jianfeng Yao, 2018. "Improving Value-at-Risk prediction under model uncertainty," Papers 1805.03890, arXiv.org, revised Jun 2020.

    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:198:y:2023:i:c:s016771522300072x. 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.