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Two classes of self-similar stable processes with stationary increments

Author

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  • Cambanis, Stamatis
  • Maejima, Makoto

Abstract

Two disjoint classes of self similar symmetric stable processes with stationary increments are studied. The first class consists of linear fractional stable processes, which are related to moving average stable processes, and the second class consists of harmonizable fractional stable processes, which are connected to harmonizable stationary stable processes. The domain of attraction of the harmonizable fractional stable processes is also discussed.

Suggested Citation

  • Cambanis, Stamatis & Maejima, Makoto, 1989. "Two classes of self-similar stable processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 305-329, August.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:305-329
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    Citations

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    Cited by:

    1. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    2. Marie-Eliette Dury & Bing Xiao, 2018. "Forecasting the Volatility of the Chinese Gold Market by ARCH Family Models and extension to Stable Models," Working Papers hal-01709321, HAL.
    3. Mazur, Stepan & Otryakhin, Dmitry & Podolskij, Mark, 2018. "Estimation of the linear fractional stable motion," Working Papers 2018:3, Örebro University, School of Business.
    4. Can, Sami Umut, 2014. "A class of asymptotically self-similar stable processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3986-4011.
    5. Hsing, Tailen, 1995. "Limit theorems for stable processes with application to spectral density estimation," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 39-71, May.

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