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The fractional mixed fractional brownian motion and fractional brownian sheet

Published online by Cambridge University Press:  17 August 2007

Charles El-Nouty
Charles El-Nouty*
Affiliation:
U.F.R. de mathématiques, Université Paris VI, 175 rue du Chevaleret, 75013 Paris, France; elnouty@ccr.jussieu.fr
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Abstract


We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.

Keywords

Fractional Brownian motionfractional Brownian sheetlower classessmall ball probabilities.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 448 - 465
Copyright
© EDP Sciences, SMAI, 2007

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