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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 23 open journal systems 


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.


Full text: PDF

Pages: 594-611

Published on: February 27, 2009
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Electronic Journal of Probability. ISSN: 1083-6489