On the Exponentials of Fractional Ornstein-Uhlenbeck Processes
Muneya Matsui, Department of Mathematics, Keio University
Narn-Rueih Shieh, Department of Mathematics, National Taiwan University
Abstract
We study the correlation decay and the expected maximal increment
(Burkholder-Davis-Gundy type inequalities) of the exponential process determined
by a fractional Ornstein-Uhlenbeck process. The method is
to apply integration by parts formula on integral representations of
fractional Ornstein-Uhlenbeck processes, and also to use Slepian's inequality.
As an application, we attempt Kahane's
T-martingale theory based on our exponential process which is shown to be of long memory.
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