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On the exponentials of fractional Ornstein-Uhlenbeck processes. (English) Zbl 1191.60048
Summary: 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.

MSC:
60G22 Fractional processes, including fractional Brownian motion
60G17 Sample path properties
60G15 Gaussian processes
60E15 Inequalities; stochastic orderings
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