IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v67y1997i2p195-211.html
   My bibliography  Save this article

Uniform large and moderate deviations for functional empirical processes

Author

Listed:
  • Dembo, Amir
  • Zajic, Tim

Abstract

For {Xi}i >= 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t >= 0}n >= 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t >= 0}n >= 1, respectively. Given a class of bounded functions F on [Sigma], we then consider the above processes as taking values in the Banach space of bounded functionals over F and obtain the corresponding (uniform over F), large and moderate deviation principles. Among the corollaries considered are functional laws of the iterated logarithm.

Suggested Citation

  • Dembo, Amir & Zajic, Tim, 1997. "Uniform large and moderate deviations for functional empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 195-211, May.
    • Handle: RePEc:eee:spapps:v:67:y:1997:i:2:p:195-211
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00006-9
    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. 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.
    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. Kurbanmuradov O. & Sabelfeld K., 2006. "Exponential bounds for the probability deviations of sums of random fields," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 211-229, October.
    2. 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.
    3. Eichelsbacher, Peter & Schmock, Uwe, 1998. "Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 233-251, September.
    4. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.

    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. Ken Duffy & David Malone, 2008. "Logarithmic asymptotics for a single-server processing distinguishable sources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 509-537, December.
    2. Zajic, Tim, 1996. "Large deviations for a class of recursive algorithms," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 135-140, February.
    3. Duffy, Ken & Lobunets, Olena & Suhov, Yuri, 2007. "Loss aversion, large deviation preferences and optimal portfolio weights for some classes of return processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 408-422.
    4. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    5. Dembo, Amir & Zeitouni, Ofer, 1996. "Large deviations for subsampling from individual sequences," Statistics & Probability Letters, Elsevier, vol. 27(3), pages 201-205, April.
    6. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    7. Włodzimierz Bryc & Amir Dembo, 1997. "Large Deviations for Quadratic Functionals of Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 10(2), pages 307-332, April.
    8. Vijay G. Subramanian, 2010. "Large Deviations of Max-Weight Scheduling Policies on Convex Rate Regions," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 881-910, November.
    9. Eichelsbacher, Peter, 1998. "Large deviations in partial sums of U-processes in stronger topologies," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 207-214, June.

    More about this item

    Keywords

    60F10 60B12 60G50;

    JEL classification:

    Statistics

    Access and download statistics

    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:67:y:1997:i:2:p:195-211. 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/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.