The fractional mixed fractional brownian motion and fractional brownian sheet
ESAIM: Probability and Statistics (2007)
- Volume: 11, page 448-465
- ISSN: 1292-8100
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topEl-Nouty, Charles. "The fractional mixed fractional brownian motion and fractional brownian sheet." ESAIM: Probability and Statistics 11 (2007): 448-465. <http://eudml.org/doc/250131>.
@article{El2007,
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.
},
author = {El-Nouty, Charles},
journal = {ESAIM: Probability and Statistics},
keywords = {Fractional Brownian motion; fractional Brownian sheet; lower
classes; small ball probabilities.; fractional Brownian motion; lower classes; small ball probabilities},
language = {eng},
month = {8},
pages = {448-465},
publisher = {EDP Sciences},
title = {The fractional mixed fractional brownian motion and fractional brownian sheet},
url = {http://eudml.org/doc/250131},
volume = {11},
year = {2007},
}
TY - JOUR
AU - El-Nouty, Charles
TI - The fractional mixed fractional brownian motion and fractional brownian sheet
JO - ESAIM: Probability and Statistics
DA - 2007/8//
PB - EDP Sciences
VL - 11
SP - 448
EP - 465
AB -
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.
LA - eng
KW - Fractional Brownian motion; fractional Brownian sheet; lower
classes; small ball probabilities.; fractional Brownian motion; lower classes; small ball probabilities
UR - http://eudml.org/doc/250131
ER -
References
top- A. Ayache, S. Leger and M. Pontier, Drap Brownien fractionnaire. Potential Anal.178 (2002) 31–43.
- A. Ayache and Y. Xiao, Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets. J. Fourier Anal. Appl.11 (2005) 407–439.
- E. Belinsky and W. Linde, Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators. J. Theoret. Probab.15 (2002) 589–612.
- C. Borell, Convex measures on locally convex space. Math. Ark. Math.12 (1974) 239–252.
- P. Cheridito, Mixed fractional Brownian motion. Bernoulli7 (2001) 913–934.
- N.J. Cutland, P.E. Kopp and W. Willinger, Stock price returns and the Joseph effect: a fractional version of the Black-Scholes model. in Seminar on Stochastic Analysis, Random Fields and Applications, Progr. Probab. E. Bolthausen, M. Dozziand F. Russo Eds., Basel: Birkhauser 36 (1995) 327–351.
- C. El-Nouty, On the lower classes of fractional Brownian motion. Studia Sci. Math. Hungar.37 (2001) 363–390.
- C. El-Nouty, Lower classes of fractional Brownian motion under Hölder norms, Limit Theorems in Probability and Statistics, Balatonlelle, 1999, I. Berkes, E. Csáki, M. Csörgő Eds., János Bolyai Mathematical Society, Budapest (2002) 7–34.
- C. El-Nouty, The fractional mixed fractional Brownian motion. Statist. Probab. Lett.65 (2003) 111–120.
- C. El-Nouty, Lower classes of integrated fractional Brownian motion. Studia Sci. Math. Hungar.41 (2004) 17–38.
- C. El-Nouty, The influence of a log-type small ball factor in the study of the lower classes. Bull. Sci. math.129 (2005) 318–338.
- F. Gassmann and D. Bürki, Experimental investigation of atmospheric dispersion over the Swiss Plain – Experiment SIESTA, Boundary-Layer Meteorology, Springer Netherlands 41 (1987) 295–307.
- F. Gassmann, P. Gaglione, S.E. Gryning, H. Hasenjäger, E. Lyck, H. Richner, B. Neiniger, S. Vogt and P. Thomas, Experimental Investigation of Atmospheric Dispersion over Complex Terrain in a Prealpine Region (experiment SIESTA) Swiss Federal Institute for Reactor Research EIR 604 (1986).
- T. Kühn and W. Linde, Optimal series representation of fractional Brownian sheets. Bernoulli8 (2002) 669–696.
- M. Ledoux and M. Talagrand, Probability in Banach spaces. Springer Verlag, Berlin (1994).
- W.V. Li, A Gaussian correlation inequality and its applications to small ball probabilities. Elect. Comm. in Probab.4 (1999) 111–118.
- W.V. Li and W. Linde, Existence of small ball constants for fractional Brownian motions. C. R. Acad. Sci. Paris326 (1998) 1329–1334.
- W.V. Li and Q.M. Shao, Gaussian Processes: Inequalities, Small Ball Probabilities and Applications, Stochastic Processes: Theory and Methods, Handbook of Statistics 19 (2001).
- M.A. Lifshits, Gaussian Random Functions. Kluwer Academic Publishers, Dordrecht (1995).
- D.M. Mason and Z. Shi, Small Deviations for Some Multi-Parameter Gaussian Processes. J. Theoret. Probab.14 (2001) 213–239.
- D. Monrad and H. Rootzen, Small values of Gaussian processes and functional laws of the iterated logarithm. Probab. Theory Related Fields101 (1995) 173–192.
- P. Révész, Random walk in random and non-random environments, World Scientific Publishing Co., Teaneck, NJ (1990).
- P.A. Samuelson, Rational theory of warrant pricing. Indust. Management Rev.6 (1965) 13–31.
- M. Talagrand, Lower classes of fractional Brownian motion. J. Theoret. Probab.9 (1996) 191–213.
- Y. Xiao and T. Zhang, Local times of fractional Brownian sheets. Probab. Theory Related Fields124 (2002) 204–226.
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