IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i6p1178-1200.html
   My bibliography  Save this article

Multivariate operator-self-similar random fields

Author

Listed:
  • Li, Yuqiang
  • Xiao, Yimin

Abstract

Multivariate random fields whose distributions are invariant under operator-scalings in both the time domain and the state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields with values in are constructed by utilizing homogeneous functions and stochastic integral representations.

Suggested Citation

  • Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1178-1200
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(11)00044-5
    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. Tatiyana V. Apanasovich & Marc G. Genton, 2010. "Cross-covariance functions for multivariate random fields based on latent dimensions," Biometrika, Biometrika Trust, vol. 97(1), pages 15-30.
    2. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    3. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    4. 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.
    5. 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.
    6. Biermé, Hermine & Lacaux, Céline, 2009. "Hölder regularity for operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2222-2248, July.
    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. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    2. Kremer, D. & Scheffler, H.-P., 2019. "Operator-stable and operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4082-4107.
    3. 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.
    4. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.
    5. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    6. Chen, Zhenlong & Wang, Jun & Wu, Dongsheng, 2020. "On intersections of independent space–time anisotropic Gaussian fields," Statistics & Probability Letters, Elsevier, vol. 166(C).
    7. Kremer, D. & Scheffler, H.-P., 2020. "About atomless random measures on δ-rings," Statistics & Probability Letters, Elsevier, vol. 164(C).
    8. Yuqiang Li & Yimin Xiao, 2012. "Occupation Time Fluctuations of Weakly Degenerate Branching Systems," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1119-1152, December.
    9. 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.

    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. 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.
    2. Kremer, D. & Scheffler, H.-P., 2019. "Operator-stable and operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4082-4107.
    3. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    4. Lee, Jeonghwa, 2021. "Hurst estimation for operator scaling random fields," Statistics & Probability Letters, Elsevier, vol. 178(C).
    5. Ben Slimane, Mourad & Alzughaibi, Imtithal & Algahtani, Obaid, 2024. "On Lp rectangular multifractal multivariate functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    6. Li, Bo & Zhang, Hao, 2011. "An approach to modeling asymmetric multivariate spatial covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1445-1453, November.
    7. Biermé, Hermine & Lacaux, Céline & Scheffler, Hans-Peter, 2011. "Multi-operator scaling random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2642-2677, November.
    8. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    9. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    10. Ip, Ryan H.L. & Li, W.K., 2017. "A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 115-119.
    11. S. De Iaco & M. Palma & D. Posa, 2013. "Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 133-150, April.
    12. Ghulam A. Qadir & Carolina Euán & Ying Sun, 2021. "Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 1-22, March.
    13. 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.
    14. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.
    15. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    16. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    17. Moreno Bevilacqua & Ronny Vallejos & Daira Velandia, 2015. "Assessing the significance of the correlation between the components of a bivariate Gaussian random field," Environmetrics, John Wiley & Sons, Ltd., vol. 26(8), pages 545-556, December.
    18. Alegría, Alfredo & Emery, Xavier, 2024. "Matrix-valued isotropic covariance functions with local extrema," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    19. 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.
    20. 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.

    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:121:y:2011:i:6:p:1178-1200. 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.