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The fractional mixed fractional brownian motionand 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 fractionalBrownian 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 sheetlowerclassessmall ball probabilities.

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