Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes

Kyoto Journal of Mathematics

Volumn 43, Issue 3, 2003, Pages 609-639

  Maejima, Makoto ^a   Sato, Ken Iti ^b  

^a KEIO UNIVERSITY   (Japan)

^b Hachiman yama 1101 5 103   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1942443727     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250283698     Document Type: Article

References (29)

1. O. E. Barndorff-Nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion), J. Royal Statist. Soc. Series B 63 (2001), 167-241.
2. P. Cheridito, H. Kawaguchi and M. Maejima, Fractional Ornstein-Uhlenbeck processes, Electric Journal of Probability 8 (2003), Paper 3, 1-14.
3. J. L. Doob, The Brownian movement and stochastic equations, Ann. of Math. 43 (1942), 351-369.
4. M. Jeanblanc, J. Pitman and M. Yor, Self-similar processes with independent increments associated with Lévy and Bessel processes, Stochastic Process. Appl. 100 (2002), 223-231.
5. Z. J. Jurek, An integral representation of operator-selfdecomposable random variables, Bull. Acad. Polonaise Sci. Sér. Sci. Math. 30 (1982), 385-393.
6. Z. J. Jurek and W. Vervaat, An integral representation for self-decomposable Banach space valued random variables, Zeit. Wahrsch. Verw. Gebiete 62 (1983), 247-262.
7. J. Lamperti, Semi-stable stochastic processes, Trans. Amer. Math. Soc. 104 (1962), 62-78.
8. N, Colloq. Math. 45 (1981), 287-300; Corrigenda 52 (1987), 167-169.
9. N, Colloq. Math. 45 (1981), 287-300; Corrigenda 52 (1987), 167-169.
10. M. Maejima and Y. Naito, Semi-selfdecomposable distributions and a new class of limit theorems, Probab. Theory Related Fields 112 (1998), 13-31.
11. M. Maejima and K. Sato, Semi-selfsimilar processes, J. Theoret. Probab. 12 (1999), 347-373.
12. M. Maejima, K. Sato and T. Watanabe, Operator semi-selfdecomposability, (C, Q)-decomposability and related nested classes, Tokyo J. Math. 22 (1999), 473-509.
13. _, Completely operator semi-selfdecomposable distributions, Tokyo J. Math. 23 (2000), 235-253.
14. T. Mikosch and R. Norvaiša, Stochastic integral equations without probability, Bernoulli 6 (2000), 401-434.
15. B. S. Rajput and J. Rosinski, Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82 (1989), 451-487.
16. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman & Hall, New York, 1994.
17. K. Sato, Self-similar processes with independent increments, Probab. Theory Related Fields 89 (1991), 285-300.
18. _, Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 1999.
19. _, Stochastic integrals in additive processes and application to semi-Lévy processes, Osaka J. Math, to appear.
20. K. Sato, T. Watanabe, K. Yamamuro and M. Yamazato, Multidimensional process of Ornstein- Uhlenbeck type with nondiagonalizable matrix in linear drift terms, Nagoya Math. J. 141 (1996), 45-78.
21. K. Sato and M. Yamazato, Stationary processes of Ornstein-Uhlenbeck type, Probability Theory and Mathematical Statistics, Fourth USSR-Japan Symp., Proc. 1982, Lecture Notes in Math. 1021, Springer, Berlin, 1983, pp. 541-551.
22. K. Sato and M. Yamazato, Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type, Stochastic Process. Appl. 17 (1984), 73-100.
23. D. Surgailis, J. Rosinski, V. Mandrekar and S. Cambanis, On the mixing structure of stationary increment and self-similar SαS processes, preprint.
24. H. Takahashi, One dimensional diffusion processes in semi-selfsimilar random environments, preprint.
25. H. Tanaka, Limit distributions for one-dimensional diffusion processes in self-similar random environments, Hydrodynamic Behavior and Interacting Particle Systems, IMA Volumes 9, Springer, 1987, pp. 189-210.
26. K. Urbanik and W. A. Woyczynski, Random integrals and Orlicz spaces, Bull. Acad. Polon. Sci. 15 (1967), 161-169.
27. T. Watanabe, Sato's conjecture on recurrence conditions for multidimensional processes of Ornstein-Uhlenbeck type, J. Math. Soc. Japan 50 (1998), 155-168.
28. n, Stochastic Process. Appl. 12 (1982), 301-312.
29. _, A characterization of certain stochastic integrals, (Tenth Conference on Stochastic Processes and Their Applications, Contributed Papers) Stochastic Process. Appl. 12 (1982), 136-136.