In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28 (1974) 174-192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.
Mots-clés : random fractals, Hausdorff dimension, Wiener process
@article{PS_2011__15__249_0,
author = {Coiffard, Claire},
title = {Random fractals generated by a local gaussian process indexed by a class of functions},
journal = {ESAIM: Probability and Statistics},
pages = {249--269},
publisher = {EDP-Sciences},
volume = {15},
year = {2011},
doi = {10.1051/ps/2010003},
mrnumber = {2870515},
zbl = {1277.60067},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2010003/}
}
TY - JOUR AU - Coiffard, Claire TI - Random fractals generated by a local gaussian process indexed by a class of functions JO - ESAIM: Probability and Statistics PY - 2011 SP - 249 EP - 269 VL - 15 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2010003/ DO - 10.1051/ps/2010003 LA - en ID - PS_2011__15__249_0 ER -
%0 Journal Article %A Coiffard, Claire %T Random fractals generated by a local gaussian process indexed by a class of functions %J ESAIM: Probability and Statistics %D 2011 %P 249-269 %V 15 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2010003/ %R 10.1051/ps/2010003 %G en %F PS_2011__15__249_0
Coiffard, Claire. Random fractals generated by a local gaussian process indexed by a class of functions. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 249-269. doi : 10.1051/ps/2010003. http://archive.numdam.org/articles/10.1051/ps/2010003/
[1] , The large deviation principle of stochastic processes. II. Theory Probab. Appl. 48 (2003) 19-44. | MR | Zbl
[2] , A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statistics 23 (1952) 493-507. | MR | Zbl
[3] and , On the Hausdorff dimension of the set generated by exceptional oscillations of a Wiener process. Studia. Sci. Math. Hungar. 33 (1997) 75-110. | MR | Zbl
[4] and , Random fractals generated by oscillations of processes with stationary and independent increments. Probability in Banach Spaces. 9 (1994) 73-90. (J. Hoffman-Jørgensen, J. Kuelbs and M.B. Marcus, eds.) | MR | Zbl
[5] and , On the fractal nature of empirical increments. Ann. Probab. 23 (1995) 355-387. | MR | Zbl
[6] , On the Hausdorff dimension of the set generated by exceptional oscillations of a two-parameter Wiener process. J. Multivariate Anal. 79 (2001) 52-70. | MR | Zbl
[7] , The Geometry of Fractal Sets. Cambridge University Press, Cambridge (1985). | MR | Zbl
[8] , Théorie de l'addition des variables aléatoires, Gauthier-Villars et Cie (1937) | JFM | Zbl
[9] , A uniform functional law of the logarithm for a local Gaussian process. Progress in Probability 55 (2003) 135-151. | MR | Zbl
[10] , A uniform functional law of the logarithm for the local empirical process. Ann. Probab. 32 (2004) 1391-1418. | MR | Zbl
[11] and , How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28 (1974) 174-192. | MR | Zbl
[12] , Some asymptotic formulas for Wiener integrals. Trans. Amer. Math. Soc. 125 (1966) 63-85. | MR | Zbl
[13] , Sharper bounds for gaussian and empirical processes. Ann. Probab. 22 (1994) 28-76. | MR | Zbl
[14] and , Weak convergence and Empirical Processes. Springer, New-York (1996). | MR | Zbl
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