Hausdorff-Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 3, pp. 373-392.
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     author = {Lucas, Alain and Thilly, Emmanuel},
     title = {Hausdorff-Besicovitch measure of fractal functional limit laws induced by {Wiener} process in {H\"older} norms},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {373--392},
     publisher = {Elsevier},
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Lucas, Alain; Thilly, Emmanuel. Hausdorff-Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 3, pp. 373-392. doi : 10.1016/j.anihpb.2005.06.001. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.06.001/

[1] A. De Acosta, On the functional form of Lévy's modulus of continuity for Brownian motion, Z. Wahr. Verw. Gebiete 69 (1985) 567-579. | MR | Zbl

[2] P. Baldi, R. Roynette, Some exact equivalents for the Brownian motion in Hölder norm, Probab. Theory Related Fields 93 (1992) 457-484. | MR | Zbl

[3] P. Berthet, Vitesses de recouvrement dans les lois fonctionnelles du logarithme itéré pour les increments du processus empirique uniforme avec applications statistiques, Thèse de l'Université Paris 6, 1996.

[4] M. Csörgő, P. Révész, How small are the increments of a Wiener process?, Stochastic Process. Appl. 8 (1979) 119-129. | MR | Zbl

[5] P. Deheuvels, M.A. Lifshits, 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

[6] P. Deheuvels, D.M. Mason, Random fractals generated by oscillations processes with stationary and independent increments, in: Hoffman-Jorgensen J., Kuelbs J., Marcus M.B. (Eds.), Probability in Banach Spaces, vol. 9, 1994, pp. 73-90. | MR | Zbl

[7] P. Deheuvels, D.M. Mason, Random fractal functional laws of the iterated logarithm, Studia Sci. Math. Hungar. 34 (1997) 89-106. | MR | Zbl

[8] P. Deheuvels, D.M. Mason, On the fractal nature of empirical increments, Ann. Probab. 23 (1995) 355-387. | MR | Zbl

[9] N. Gorn, M.A. Lifshits, Chung's law and Csáki function, J. Theoret. Probab. 12 (1999) 399-420. | MR | Zbl

[10] K.J. Falconer, Fractal Geometry, Mathematical Foundations and Applications, Wiley, New York, 1990. | MR | Zbl

[11] D. Khoshnevisan, Y. Peres, Y. Xiao, Limsup random fractals, Electron. J. Probab. 5 (2000) 1-24. | MR | Zbl

[12] J. Kuelbs, W. Li, Small ball estimates for Brownian motion and the Brownian sheet, J. Theoret. Probab. 6 (1993) 547-577. | MR | Zbl

[13] J. Kuelbs, W. Li, M. Talagrand, Liminf results for Gaussian samples and Chung's functional LIL, Ann. Probab. 22 (1994) 1879-1903. | MR | Zbl

[14] A. Lucas, Hausdorff-Besicovitch measure for random fractals of Chung's type, Math. Proc. Cambridge Philos. Soc. 133 (2002) 487-513. | MR | Zbl

[15] S. Orey, S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail?, Math. Proc. Cambridge Philos. Soc. 49 (1974) 31-39. | MR | Zbl

[16] G. Shorack, J.A. Wellner, Empirical Processes with Applications to Statistics, John Wiley & Sons, 1986. | MR | Zbl

[17] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahr. Verw. Gebiete 3 (1964) 211-226. | MR | Zbl

[18] Q. Wei, Functional modulus of continuity for Brownian motion in Hölder norm, Chinese Ann. Math. Ser. B 22 (2001) 223-232. | MR | Zbl

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