Short and Long Memory Fractional Ornstein–Uhlenbeck α-Stable Processes

REFERENCES

• Beran , J. Statistics for Long-Memory Processes; Chapman & Hall : New York , 1994 .
   Google Scholar
• Burnecki , K. ; Maejima , M. ; Weron , A. The Lamperti transformation for self-similar processes . Yokohama Math. J. 1997 , 44 , 25 – 42 .
   Google Scholar
• Cheridito , P. ; Kawaguchi , H. ; Maejima , M. Fractional Ornstein–Uhlenbeck processes . Electron. J. Probab. 2003 , 8 , 1 – 14 .
   Google Scholar
• Doukhan , P. ; Oppenheim , G. ; Taqqu , M.S. Theory and Applications of Long-Range Dependence; Birkhäuser : Boston , 2003 .
   Google Scholar
• Janicki , A. ; Weron , A. Simulation and Chaotic Behaviour of α-Stable Stochastic Processes; Marcel Dekker : New York , 1994 .
   Google Scholar
• Lamperti , J.W. Semi-stable stochastic processes . Trans. Amer. Math. Soc. 1962 , 104 , 62 – 78 .
   Google Scholar
• Lévy , J.B. ; Taqqu , M.S. A Characterization of the asymptotic behavior of stationary stable processes. In Stable Processes and Related Topics; Cambanis , S. ; Samorodnitsky , G. ; Taqqu , M.S. , Eds.; Birkhäuser : Boston , 1991; pp. 181–198.
   Google Scholar
• Maejima , M. ; Yamamoto , K. Long-memory stable Ornstein–Uhlenbeck processes . Electron. J. Probab. 2003 , 8 , 1 – 18 .
   Google Scholar
• Magdziarz , M. The dependence structure of the fractional Ornstein–Uhlenbeck process . Prob. and Math. Stat. 2005 , 25 , 97 – 104 .
   Google Scholar
• Rosinski , J. ; Zak , T. Simple conditions for mixing of infinitely divisible processes . Stochastic Process. Appl. 1996 , 61 , 277 – 288 .
   Google Scholar
• Samorodnitsky , G. ; Taqqu , M.S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance; Chapman and Hall : New York , 1994 .
   Google Scholar