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Operator-self-similar stable processes

Author

Listed:
  • Maejima, Makoto
  • Mason, J. David

Abstract

Operator-self-similar processes are studied and several examples of operator-self-similar and stable (in the ordinary sense or in the sense of operator-stable) processes are constructed. Limit theorems for such processes are also shown.

Suggested Citation

  • Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:1:p:139-163
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    Citations

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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. Meerschaert, Mark M. & Scheffler, Hans-Peter, 1999. "Spectral decomposition for operator self-similar processes and their generalized domains of attraction," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 71-80, November.
    4. Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.
    5. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
    6. 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.
    7. Gustavo Didier & Vladas Pipiras, 2012. "Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 25(2), pages 353-395, June.
    8. Saigo, Tatsuhiko & Tamura, Yozo, 2006. "Operator semi-self-similar processes and their space-scaling matrices," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 675-681, April.
    9. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
    10. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.
    11. Lee, Jeonghwa, 2021. "Hurst estimation for operator scaling random fields," Statistics & Probability Letters, Elsevier, vol. 178(C).
    12. Patrice Abry & B. Cooper Boniece & Gustavo Didier & Herwig Wendt, 2023. "Wavelet eigenvalue regression in high dimensions," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 1-32, April.
    13. Wensheng Wang, 2024. "The Moduli of Continuity for Operator Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2097-2120, September.
    14. Lee, Jeonghwa, 2020. "Wavelet estimation in OFBM: Choosing scale parameter in different sampling methods and different parameter values," Statistics & Probability Letters, Elsevier, vol. 166(C).
    15. Characiejus, Vaidotas & Račkauskas, Alfredas, 2014. "Operator self-similar processes and functional central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2605-2627.

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