Geodesic
The fractional mixed fractional brownian motion and fractional brownian sheet
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 448-465

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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.

DOI : 10.1051/ps:2007029
Classification : 60F15, 60G15
Keywords: fractional brownian motion, fractional brownian sheet, lower classes, small ball probabilities 
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     author = {El-Nouty, Charles},
     title = {The fractional mixed fractional brownian motion and fractional brownian sheet},
     journal = {ESAIM: Probability and Statistics},
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     publisher = {EDP-Sciences},
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     year = {2007},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007029/}
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El-Nouty, Charles. The fractional mixed fractional brownian motion and fractional brownian sheet. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 448-465. doi: 10.1051/ps:2007029

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