IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v92y2001i1p11-30.html
   My bibliography  Save this article

Non-linear functionals of the Brownian bridge and some applications

Author

Listed:
  • Berzin-Joseph, Corinne
  • León, José R.
  • Ortega, Joaquín

Abstract

Let {bF(t),t[set membership, variant][0,1]} be an F-Brownian bridge process. We study the asymptotic behaviour of non-linear functionals of regularizations by convolution of this process and apply these results to the estimation of the variance of a non-homogeneous diffusion and to the convergence of the number of crossings of a level by the regularized process to a modification of the local time of the Brownian bridge as the regularization parameter goes to 0.

Suggested Citation

  • Berzin-Joseph, Corinne & León, José R. & Ortega, Joaquín, 2001. "Non-linear functionals of the Brownian bridge and some applications," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 11-30, March.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:11-30
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00068-5
    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. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    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. Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.
    2. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    3. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    4. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
    5. Miguel A. Arcones, 1999. "The Law of the Iterated Logarithm over a Stationary Gaussian Sequence of Random Vectors," Journal of Theoretical Probability, Springer, vol. 12(3), pages 615-641, July.
    6. Nourdin, Ivan & Nualart, David & Peccati, Giovanni, 2021. "The Breuer–Major theorem in total variation: Improved rates under minimal regularity," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 1-20.
    7. Jun Yuan & Haowei Wang & Szu Hui Ng & Victor Nian, 2020. "Ship Emission Mitigation Strategies Choice Under Uncertainty," Energies, MDPI, vol. 13(9), pages 1-20, May.
    8. Nualart, D. & Ortiz-Latorre, S., 2008. "Central limit theorems for multiple stochastic integrals and Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 614-628, April.
    9. Mikko S. Pakkanen & Anthony Réveillac, 2014. "Functional limit theorems for generalized variations of the fractional Brownian sheet," CREATES Research Papers 2014-14, Department of Economics and Business Economics, Aarhus University.
    10. Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011. "Quantitative Breuer-Major theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 793-812, April.
    11. Ivan Nourdin & Murad S. Taqqu, 2014. "Central and Non-central Limit Theorems in a Free Probability Setting," Journal of Theoretical Probability, Springer, vol. 27(1), pages 220-248, March.
    12. Doukhan, P. & Pommeret, D. & Reboul, L., 2015. "Data driven smooth test of comparison for dependent sequences," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 147-165.
    13. Sibbertsen, Philipp, 2000. "Robust CUSUM-M test in the presence of long-memory disturbances," Technical Reports 2000,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Malte Knüppel, 2015. "Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 270-281, April.
    15. Marinucci, Domenico & Peccati, Giovanni, 2008. "High-frequency asymptotics for subordinated stationary fields on an Abelian compact group," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 585-613, April.
    16. Soulier, Philippe, 2001. "Moment bounds and central limit theorem for functions of Gaussian vectors," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 193-203, September.
    17. Tailen Hsing, 2000. "Linear Processes, Long-Range Dependence and Asymptotic Expansions," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 19-29, January.
    18. Johann Gehringer & Xue-Mei Li, 2022. "Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 35(1), pages 426-456, March.
    19. N. N. Leonenko & M. D. Ruiz-Medina, 2008. "Gaussian Scenario for the Heat Equation with Quadratic Potential and Weakly Dependent Data with Applications," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 595-620, December.
    20. León, José & Ludeña, Carenne, 2007. "Limits for weighted p-variations and likewise functionals of fractional diffusions with drift," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 271-296, March.

    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:92:y:2001:i:1:p:11-30. 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.