IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i6p1823-1844.html
   My bibliography  Save this article

Continuity in the Hurst index of the local times of anisotropic Gaussian random fields

Author

Listed:
  • Wu, Dongsheng
  • Xiao, Yimin

Abstract

Let be a family of (N,d)-anisotropic Gaussian random fields with generalized Hurst indices H=(H1,...,HN)[set membership, variant](0,1)N. Under certain general conditions, we prove that the local time of is jointly continuous whenever . Moreover we show that, when H approaches H0, the law of the local times of XH(t) converges weakly [in the space of continuous functions] to that of the local time of XH0. The latter theorem generalizes the result of [M. Jolis, N. Viles, Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion, J. Theoret. Probab. 20 (2007) 133-152] for one-parameter fractional Brownian motions with values in to a wide class of (N,d)-Gaussian random fields. The main argument of this paper relies on the recently developed sectorial local nondeterminism for anisotropic Gaussian random fields.

Suggested Citation

  • Wu, Dongsheng & Xiao, Yimin, 2009. "Continuity in the Hurst index of the local times of anisotropic Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1823-1844, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1823-1844
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00141-5
    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. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    2. S. Davies & P. Hall, 1999. "Fractal analysis of surface roughness by using spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 3-37.
    3. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    4. Eisenbaum, Nathalie & Khoshnevisan, Davar, 2002. "On the most visited sites of symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 241-256, October.
    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. Giordano, Luca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2020. "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7396-7430.

    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. Lim, S.C. & Teo, L.P., 2009. "Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1325-1356, April.
    2. Sönmez, Ercan, 2018. "The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 426-444.
    3. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
    4. Moreno Bevilacqua & Alfredo Alegria & Daira Velandia & Emilio Porcu, 2016. "Composite Likelihood Inference for Multivariate Gaussian Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 448-469, September.
    5. Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
    6. Frank Davenport, 2017. "Estimating standard errors in spatial panel models with time varying spatial correlation," Papers in Regional Science, Wiley Blackwell, vol. 96, pages 155-177, March.
    7. Sun, Ying & Chang, Xiaohui & Guan, Yongtao, 2018. "Flexible and efficient estimating equations for variogram estimation," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 45-58.
    8. Daniel Griffith, 2010. "Modeling spatio-temporal relationships: retrospect and prospect," Journal of Geographical Systems, Springer, vol. 12(2), pages 111-123, June.
    9. Oleksandr Gromenko & Piotr Kokoszka & Matthew Reimherr, 2017. "Detection of change in the spatiotemporal mean function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 29-50, January.
    10. Villez, Kris & Del Giudice, Dario & Neumann, Marc B. & Rieckermann, Jörg, 2020. "Accounting for erroneous model structures in biokinetic process models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    11. Myoungji Lee & Marc G. Genton & Mikyoung Jun, 2016. "Testing Self-Similarity Through Lamperti Transformations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 426-447, September.
    12. M. Ruiz-Medina & J. Angulo & G. Christakos & R. Fernández-Pascual, 2016. "New compactly supported spatiotemporal covariance functions from SPDEs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 125-141, March.
    13. Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.
    14. Montero, José-María, 2018. "Geostatistics: Unde venis et quo vadis? /Geoestadística:¿De dónde vienes y a dónde vas?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 81-106, Enero.
    15. Tata Subba Rao & Granville Tunnicliffe Wilson & Tata Subba Rao & Gyorgy Terdik, 2017. "On the Frequency Variogram and on Frequency Domain Methods for the Analysis of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 308-325, March.
    16. Gneiting, Tilmann, 2002. "Compactly Supported Correlation Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 493-508, November.
    17. Hong, Yiping & Zhou, Zaiying & Yang, Ying, 2020. "Hypothesis testing for the smoothness parameter of Matérn covariance model on a regular grid," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    18. Li, Yuqiang, 2011. "Fluctuation limits of site-dependent branching systems in critical and large dimensions," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1604-1611, November.
    19. Marcus L. Nascimento & Kelly C. M. Gonçalves & Mario Jorge Mendonça, 2023. "Spatio-Temporal Instrumental Variables Regression with Missing Data: A Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 29-47, June.
    20. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Scaling transition for nonlinear random fields with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2751-2779.

    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:119:y:2009:i:6:p:1823-1844. 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.