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.
"On the Exponentials of Fractional Ornstein-Uhlenbeck Processes." Electron. J. Probab. 14 594 - 611, 2009. https://doi.org/10.1214/EJP.v14-628