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[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes

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  • Maejima, Makoto
  • Ueda, Yohei

Abstract

The concept of selfdecomposability has been generalized to that of [alpha]-selfdecomposability, , by many authors. We first mention the existing results on the class of [alpha]-selfdecomposable distributions and investigate the remaining problems. We give complete characterizations by stochastic integrals with respect to Lévy processes for the case 1

Suggested Citation

  • Maejima, Makoto & Ueda, Yohei, 2010. "[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2363-2389, December.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:12:p:2363-2389
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    1. repec:dau:papers:123456789/1380 is not listed on IDEAS
    2. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    3. Wolfe, Stephen James, 1982. "On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 301-312, May.
    4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
    5. Jurek, Zbigniew J. & Schreiber, Bertram M., 1992. "Fourier transforms of measures from the classes [beta]' -2," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 194-211, May.
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