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.
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