Electronic Journal of Probability

On the Exponentials of Fractional Ornstein-Uhlenbeck Processes

Muneya Matsui and Narn-Rueih Shieh

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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.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 23, 594-611.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G17: Sample path properties 60G15: Gaussian processes
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G10: Stationary processes

Long memory (Long range dependence) Fractional Brownian motion Fractional Ornstein-Uhlenbeck process Exponential process Burkholder-Davis-Gundy inequalities

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Matsui, Muneya; Shieh, Narn-Rueih. On the Exponentials of Fractional Ornstein-Uhlenbeck Processes. Electron. J. Probab. 14 (2009), paper no. 23, 594--611. doi:10.1214/EJP.v14-628. https://projecteuclid.org/euclid.ejp/1464819484

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