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Multivariate operator-self-similar random fields

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. Chen, Zhenlong & Wang, Jun & Wu, Dongsheng, 2020. "On intersections of independent space–time anisotropic Gaussian fields," Statistics & Probability Letters, Elsevier, vol. 166(C).
    6. 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.
    7. 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.
    8. Kremer, D. & Scheffler, H.-P., 2020. "About atomless random measures on δ-rings," Statistics & Probability Letters, Elsevier, vol. 164(C).
    9. 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.

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