IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i11p2486-2491.html
   My bibliography  Save this article

Moderate deviation principle for Brownian motions on the unit sphere in Rd

Author

Listed:
  • Chen, Lei
  • Gao, Fuqing

Abstract

In this paper, we obtain the moderate deviation principle for a sequence of Brownian motions defined on the unit sphere in Rd by using the cumulant method introduced by Puhalskii (1994b) and generalize it to Ornstein–Uhlenbeck processes taking values on the unit sphere in Rd.

Suggested Citation

  • Chen, Lei & Gao, Fuqing, 2013. "Moderate deviation principle for Brownian motions on the unit sphere in Rd," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2486-2491.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2486-2491
    DOI: 10.1016/j.spl.2013.07.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213002599
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.07.010?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. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    2. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
    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. Xue, Xiaofeng, 2021. "Moderate deviations of density-dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 49-80.
    2. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.
    3. Ma, Xiaocui & Xi, Fubao, 2017. "Moderate deviations for neutral stochastic differential delay equations with jumps," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 97-107.
    4. Dembo, Amir & Zajic, Tim, 1995. "Large deviations: From empirical mean and measure to partial sums process," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 191-224, June.
    5. Benoist, Tristan & Fatras, Jan-Luka & Pellegrini, Clément, 2023. "Limit theorems for quantum trajectories," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 288-310.
    6. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    7. I. G. Grama & E. Haeusler, 2006. "An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales," Journal of Theoretical Probability, Springer, vol. 19(1), pages 1-44, January.
    8. Ulrich Horst & Jan Wezelburger, 2006. "Non-ergodic Behavior in a Financial Market with Interacting Investors," 2006 Meeting Papers 229, Society for Economic Dynamics.
    9. Klebaner, F. C. & Liptser, R., 1999. "Moderate deviations for randomly perturbed dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 157-176, April.
    10. Xiequan Fan & Ion Grama & Quansheng Liu, 2020. "Cramér Moderate Deviation Expansion for Martingales with One-Sided Sakhanenko’s Condition and Its Applications," Journal of Theoretical Probability, Springer, vol. 33(2), pages 749-787, June.
    11. Bouzebda, Salim & Slaoui, Yousri, 2019. "Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 17-28.
    12. Franziska Kühn & René L. Schilling, 2016. "Moderate Deviations and Strassen’s Law for Additive Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 632-652, June.
    13. Xue, Xiaofeng & Zhao, Linjie, 2024. "Moderate deviations for the current and tagged particle in symmetric simple exclusion processes," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    14. Anatolii A. Puhalskii & Alexander A. Vladimirov, 2007. "A Large Deviation Principle for Join the Shortest Queue," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 700-710, August.
    15. Fan, Xiequan & Grama, Ion & Liu, Quansheng & Shao, Qi-Man, 2020. "Self-normalized Cramér type moderate deviations for stationary sequences and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5124-5148.

    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:83:y:2013:i:11:p:2486-2491. 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.