Long-memory stable ornstein-uhlenbeck processes

Electronic Journal of Probability

Volumn 8, Issue , 2003, Pages 1-18

  Maejima, Makoto ^a   Yamamoto, Kenji ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Langevin equation; Linear fractional stable motion; Long range dependence; Selfsimilar process

Indexed keywords

EID: 10644291517     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v8-168     Document Type: Article

References (13)

1. Adler, R.J., Cambanis, S. and Samorodnitsky, G. (1990): On stable Markov processes, Stock. Proc. Appl. 34, 1-17.
2. Astrauskas, A., Levy, J.B. and Taqqu, M.S. (1991): The asymptotic dependence structure of the linear fractional Levy motion, Lietuvos Matematikos Rinkinys (Lithuanian Mathematical Journal) 31(1), 1-28.
3. Cheridito, P., Kawaguchi, H. and Maejima, M. (2003): Fractional Ornstein-Uhlenbeck processes, Electron. J. Probab. 8, paper no. 3, 1-14.
4. Cox, D.R. (1984): Long-range dependence: A review, In Statistics: An Appraisal, The Iowa University Press, 55-74.
5. Doob, J.L. (1942): The Brownian movement and stochastic equations, Ann. Math. 43, 351-369.
6. Maejima, M. (1983): On a class of self-similar processes, Z. Wahrsheinlichkeitstkeorie verw. Gebiete 62, 235-245.
7. Maejima, M. (1983): A self-similar process with nowhere bounded sample paths, Z. Wahrshein-lichkeitstheorie verw. Gebiete 65, 115-119.
8. Maruyama, G. (1970): Infinitely divisible processes, Theory Probab. Appl. 15, 1-22.
9. Rosinski, J. and Zak, T. (1995): Simple conditions for mixing of infinitely divisible processes, Stock. Proc. Appl. 61, 277-288.
10. Samorodnitsky, G. (2002): Long Range Dependence, Heavy Tails and Rare Events, Lecture Notes Series, No. 12, MaPhySto, University of Aarhus.
11. Samorodnitsky, G. and Taqqu, M.S. (1994): Stable Non-Gaussian Random Processes, Chapman & Hall.
12. Sato, K. (1999): Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press.
13. Surgailis, D., Rosinski, J., Mandrekar, V. and Cambanis, S. (2001): On the mixing structure of stationary increment and self-similer SaS processes, Preprint.