[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2006.21.4.787

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)

Publication Information

Communications of the Korean Mathematical Society / v.21, no.4, 2006 , pp. 787-794 More about this Journal

Abstract

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.

Keywords

Levy process; subordination; stability; self-decomposability; semi-stability; semi-selfdecomposability;

Citations & Related Records

Reference

1	O. E. Barndorff-Nielsen, J. Pedersen, and K. Sato, Multivariate subordination, self- decomposability and stability., Adv. Appl. Probab. 33 (2001), 160-187 DOI ScienceOn
2	L. Bondesson, Generalized Gamma Convolutions and Related Classes of Distribution Densities., Lecture Notes in Statistics, Vol 76. Springer, New York., 1992
3	M. Maejima and Y. Naito, Semi-selfdecomposable distributions and a new class of limit theorems, Probab.Theory Related Fields 112 (1998), 13-31 DOI
4	B. Ramachandran and K. Lau, Functional Equations in Probability Theory, Academic Press, 1991
5	K. Sato, Processes and Infinitely Divisible Distributions., Cambridge University Press, Cambridge, 1999
6	K. Sato, Subordination and self-decomposability., Statistics & Probability Letters 54 (2001), 317-324 DOI ScienceOn
7	G. S. Choi, Criteria for recurrence and transience of semistable processes, Nagoya. Math. J. 134 (1994), 91-106 DOI
8	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