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Distributions of selfsimilar and semi-selfsimilar processes with independent increments

Author

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  • Maejima, Makoto
  • Sato, Ken-iti
  • Watanabe, Toshiro

Abstract

Relationships between marginal and joint distributions of selfsimilar processes with independent increments are shown in terms of the Urbanik-Sato-type nested subclasses of the class of selfdecomposable distributions. Similar results are also shown for semi-selfsimilar processes with independent increments.

Suggested Citation

  • Maejima, Makoto & Sato, Ken-iti & Watanabe, Toshiro, 2000. "Distributions of selfsimilar and semi-selfsimilar processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 395-401, May.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:4:p:395-401
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    References listed on IDEAS

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    1. Sato, Ken-iti, 1980. "Class L of multivariate distributions and its subclasses," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 207-232, June.
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    Cited by:

    1. Becker-Kern, Peter & Pap, Gyula, 2008. "Parameter estimation of selfsimilarity exponents," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 117-140, January.
    2. Colino, Jesús P., 2008. "New stochastic processes to model interest rates : LIBOR additive processes," DES - Working Papers. Statistics and Econometrics. WS ws085316, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Akita, Koji & Maejima, Makoto, 2002. "On certain self-decomposable self-similar processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 53-59, August.
    4. Becker-Kern, Peter, 2004. "Random integral representation of operator-semi-self-similar processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 327-344, February.
    5. Toshiro Watanabe, 2002. "Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes," Journal of Theoretical Probability, Springer, vol. 15(3), pages 631-665, July.
    6. Ole E. Barndorff-Nielsen & Makoto Maejima & Ken-iti Sato, 2006. "Infinite Divisibility for Stochastic Processes and Time Change," Journal of Theoretical Probability, Springer, vol. 19(2), pages 411-446, June.

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