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On the Exponentials of Fractional Ornstein-Uhlenbeck Processes

   
@article{EJP628,
	author = {Muneya Matsui and Narn-Rueih Shieh},
	title = {On the Exponentials of Fractional Ornstein-Uhlenbeck Processes},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {Long memory (Long range dependence), Fractional Brownian motion, Fractional Ornstein-Uhlenbeck process,  Exponential process, Burkholder-Davis-Gundy inequalities.},
	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.},
	pages = {no. 23, 594-611},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-628},    
        url = {http://ejp.ejpecp.org/article/view/628}}