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2009 On the Exponentials of Fractional Ornstein-Uhlenbeck Processes
Muneya Matsui, Narn-Rueih Shieh
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Electron. J. Probab. 14: 594-611 (2009). DOI: 10.1214/EJP.v14-628


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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Muneya Matsui. Narn-Rueih Shieh. "On the Exponentials of Fractional Ornstein-Uhlenbeck Processes." Electron. J. Probab. 14 594 - 611, 2009.


Accepted: 27 February 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60048
MathSciNet: MR2486815
Digital Object Identifier: 10.1214/EJP.v14-628

Primary: 60G15 , 60G17
Secondary: 60G10 , 62M10

Keywords: Burkholder-Davis-Gundy inequalities , Exponential process , fractional Brownian motion , fractional Ornstein-Uhlenbeck process , Long memory (Long range dependence)

Vol.14 • 2009
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