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http://dx.doi.org/10.4134/BKMS.2010.47.3.483

A NOTE ON SEMI-SELFDECOMPOSABILITY AND OPERATOR SEMI-STABILITY IN SUBORDINATION  

Choi, Gyeong-Suk (Department of mathematics Kangwon National University)
Kim, Yun-Kyong (Department of Information & Communication Engineering Dongshin University)
Joo, Sang-Yeol (Department of mathematics Kangwon National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 483-490 More about this Journal
Abstract
Some results on inheritance of operator semi-selfdecomposability and its decreasing subclass property from subordinator to subordinated in subordination of a L$\acute{e}$evy process are given. A main result is an extension of results of [5] to semi-selfdecomposable subordinator. Its consequence is discussed.
Keywords
operator semi-selfdecomposability; operator semi-stability; strict operator semi-stability; subordination; semi-selfdecomposability;
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1 G. S. Choi, Criteria for recurrence and transience of semistable processes, Nagoya Math. J. 134 (1994), 91-106.
2 T. J. Kozubowski, A note on self-decomposability of stable process subordinated to self-decomposable subordinator, Statist. Probab. Lett. 74 (2005), no. 1, 89-91.   DOI   ScienceOn
3 A. Luczak, Operator semistable probability measures on $R^{N}$, Colloq. Math. 45 (1981), no. 2, 287-300
4 A. Luczak, Operator semistable probability measures on $R^{N}$, Corrigenda, Colloq. Math. 52 (1987), no. 1, 167-169.
5 M. Maejima and Y. Naito, Semi-selfdecomposable distributions and a new class of limit theorems, Probab. Theory Related Fields 112 (1998), no. 1, 13-31.   DOI
6 M. Maejima, K. Sato, and T. Watanabe, Operator semi-selfdecomposability, (C,Q)-decomposability and related nested classes, Tokyo J. Math. 22 (1999), no. 2, 473-509.   DOI
7 K. Sato, Selfdecomposability and semi-selfdecomposability in subordination of coneparameter convolution semigroups, Tokyo J. Math. 32 (2009), no. 1, 81-90.   DOI
8 G. S. Choi, S. Y. Joo, and Y. K. Kim, Subordination, self-decomposability and semistability, Commun. Korean Math. Soc. 21 (2006), no. 4, 787-794.   DOI   ScienceOn
9 G. S. Choi, Characterization of strictly operator semi-stable distributions, J. Korean Math. Soc. 38 (2001), no. 1, 101-123.
10 G. S. Choi, Some results on subordination, selfdecomposability and operator semi-stability, Statist. Probab. Lett. 78 (2008), no. 6, 780-784.   DOI   ScienceOn
11 C. Halgreen, Self-decomposability of the generalized inverse Gaussian and hyperbolic distributions, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 1, 13-17.   DOI
12 R. Jajte, Semi-stable probability measures on RN, Studia Math. 61 (1977), no. 1, 29-39.
13 T. J. Kozubowski, A note on self-decomposability of stable process subordinated to self-decomposable subordinator, Statist. Probab. Lett. 73 (2005), no. 4, 343-345   DOI   ScienceOn
14 J. Pedersen and K. Sato, Relations between cone-parameter Levy processes and convolution semigroups, J. Math. Soc. Japan 56 (2004), no. 2, 541-559.   DOI
15 M. Maejima, K. Sato, and T. Watanabe, Completely operator semi-selfdecomposable distributions, Tokyo J. Math. 23 (2000), no. 1, 235-253.   DOI
16 M. Maejima, K. Sato, and T. Watanabe, Distributions of selfsimilar and semi-selfsimilar processes with independent increments, Statist. Probab. Lett. 47 (2000), no. 4, 395-401.   DOI   ScienceOn
17 J. Pedersen and K. Sato, Cone-parameter convolution semigroups and their subordination, Tokyo J. Math. 26 (2003), no. 2, 503-525.   DOI
18 K. Sato, Levy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999.
19 K. Sato, Subordination and self-decomposability, Statist. Probab. Lett. 54 (2001), no. 3, 317-324.   DOI   ScienceOn
20 O. E. Barndorff-Nielsen, M. Maejima, and K. Sato, Infinite divisibility for stochastic processes and time change, J. Theoret. Probab. 19 (2006), no. 2, 411-446.   DOI
21 O. E. Barndorff-Nielsen, J. Pedersen, and K. Sato, Multivariate subordination, self-decomposability and stability, Adv. in Appl. Probab. 33 (2001), no. 1, 160-187.   DOI   ScienceOn