Electronic Journal of Probability
- Electron. J. Probab.
- Volume 8 (2003), paper no. 19, 18 p.
Long-Memory Stable Ornstein-Uhlenbeck Processes
The solution of the Langevin equation driven by a Lévy process noise has been well studied, under the name of Ornstein-Uhlenbeck type process. It is a stationary Markov process. When the noise is fractional Brownian motion, the covariance of the stationary solution process has been studied by the first author with different coauthors. In the present paper, we consider the Langevin equation driven by a linear fractional stable motion noise, which is a selfsimilar process with long-range dependence but does not have finite variance, and we investigate the dependence structure of the solution process.
Electron. J. Probab., Volume 8 (2003), paper no. 19, 18 p.
First available in Project Euclid: 23 May 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G10: Stationary processes 60G18: Self-similar processes
Maejima, Makoto; Yamamoto, Kenji. Long-Memory Stable Ornstein-Uhlenbeck Processes. Electron. J. Probab. 8 (2003), paper no. 19, 18 p. doi:10.1214/EJP.v8-168. https://projecteuclid.org/euclid.ejp/1464037592