| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 448 - 465 | |
| DOI | https://doi.org/10.1051/ps:2007029 | |
| Published online | 17 August 2007 | |
The fractional mixed fractional brownian motion and fractional brownian sheet
U.F.R. de mathématiques, Université Paris VI, 175 rue du
Chevaleret, 75013 Paris, France; elnouty@ccr.jussieu.fr
Received:
29
September
2005
Revised:
2
May
2006
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.
Mathematics Subject Classification: 60F15 / 60G15
Key words: Fractional Brownian motion / fractional Brownian sheet / lower classes / small ball probabilities.
© EDP Sciences, SMAI, 2007
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