대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
  • /
  • Pages.787-794
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  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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SUBORDINATION, SELF-DECOMPOSABILITY AND SEMI-STABILITY

  • Choi, Gyeong-Suk (Institute of Basic Science Kangwon National University) ;
  • Joo, Sang-Yeol (Department of Statistics Kangwon National University) ;
  • Kim, Yun-Kyong (Department of Information & Communication Engineering Dongshin University)
  • 발행 : 2006.10.31
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초록

Two main results are presented in relation to subordination, self-decomposability and semi-stability. One of the result is that strict semi-stability of subordinand process by selfdecomposable subordinator gives semi-selfdecomposability of the subordinated process. The second result is a sufficient condition for any subordinated process arising from a semi-stable subordinand and a semi-stable subordinator to be semi-selfdecomposable.

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참고문헌

  1. O. E. Barndorff-Nielsen, J. Pedersen, and K. Sato, Multivariate subordination, self- decomposability and stability., Adv. Appl. Probab. 33 (2001), 160-187 https://doi.org/10.1239/aap/999187902
  2. O. E. Barndorff-Nielsen and N. Shephard, Modeling by Levy processes for financial econometrics. In: Barndorff-Nielsen, O. E., Mikosch, T., Resnick, S. I. (Eds) , Levy Processes- Theory and Applications, Birkhauser, Boston, 2001, pp. 283-318
  3. L. Bondesson, Generalized Gamma Convolutions and Related Classes of Distribution Densities., Lecture Notes in Statistics, Vol 76. Springer, New York., 1992
  4. G. S. Choi, Criteria for recurrence and transience of semistable processes, Nagoya. Math. J. 134 (1994), 91-106 https://doi.org/10.1017/S0027763000004876
  5. M. Maejima and Y. Naito, Semi-selfdecomposable distributions and a new class of limit theorems, Probab.Theory Related Fields 112 (1998), 13-31 https://doi.org/10.1007/s004400050181
  6. B. Ramachandran and K. Lau, Functional Equations in Probability Theory, Academic Press, 1991
  7. K. Sato, Processes and Infinitely Divisible Distributions., Cambridge University Press, Cambridge, 1999
  8. K. Sato, Subordination and self-decomposability., Statistics & Probability Letters 54 (2001), 317-324 https://doi.org/10.1016/S0167-7152(01)00110-9

피인용 문헌

  1. Some results on subordination, selfdecomposability and operator semi-stability vol.78, pp.6, 2008, https://doi.org/10.1016/j.spl.2007.09.044