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Operator-stable and operator-self-similar random fields

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  • Kremer, D.
  • Scheffler, H.-P.

Abstract

Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields X={X(t):t∈Rd} with values in Rm are invariant in law under operator-scaling in both the time-domain and the state-space. The construction is based on operator-stable random measures utilizing certain homogeneous functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:4082-4107
    DOI: 10.1016/j.spa.2018.11.013
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    References listed on IDEAS

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    1. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    2. 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.
    3. 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.
    4. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
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    Cited by:

    1. Kremer, D. & Scheffler, H.-P., 2020. "About atomless random measures on δ-rings," Statistics & Probability Letters, Elsevier, vol. 164(C).
    2. Chen, Zhenlong & Xu, Peng, 2024. "Higher-order derivative of local times for space–time anisotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 214(C).

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