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 Electronic Journal of Probability > Vol. 8 (2003) > Paper 19 open journal systems 


Long-Memory Stable Ornstein-Uhlenbeck Processes

Makoto Maejima, Department of Mathematics, Keio University
Kenji Yamamoto, Department of Mathematics, Keio University


Abstract
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.


Full text: PDF

Pages: 1--18

Published on: November 20, 2003
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Electronic Journal of Probability. ISSN: 1083-6489