Hausdorff–Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms

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1. [1] A. de Acosta, On the functional form of Lévy's modulus of continuity for Brownian motion, Z. Wahr. Verw. Gebiete69 (1985) 567-579. Zbl0548.60034MR791912
2. [2] P. Baldi, R. Roynette, Some exact equivalents for the Brownian motion in Hölder norm, Probab. Theory Related Fields93 (1992) 457-484. Zbl0767.60078MR1183887
3. [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. [4] M. Csörgő, P. Révész, How small are the increments of a Wiener process?, Stochastic Process. Appl.8 (1979) 119-129. Zbl0387.60032MR520824
5. [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. Zbl0908.60012MR1454103
6. [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. Zbl0809.60042MR1308511
7. [7] P. Deheuvels, D.M. Mason, Random fractal functional laws of the iterated logarithm, Studia Sci. Math. Hungar.34 (1997) 89-106. Zbl0916.60037MR1645150
8. [8] P. Deheuvels, D.M. Mason, On the fractal nature of empirical increments, Ann. Probab.23 (1995) 355-387. Zbl0835.60024MR1330774
9. [9] N. Gorn, M.A. Lifshits, Chung's law and Csáki function, J. Theoret. Probab.12 (1999) 399-420. Zbl0937.60013MR1684751
10. [10] K.J. Falconer, Fractal Geometry, Mathematical Foundations and Applications, Wiley, New York, 1990. Zbl0871.28009MR1102677
11. [11] D. Khoshnevisan, Y. Peres, Y. Xiao, Limsup random fractals, Electron. J. Probab.5 (2000) 1-24. Zbl0949.60025MR1743726
12. [12] J. Kuelbs, W. Li, Small ball estimates for Brownian motion and the Brownian sheet, J. Theoret. Probab.6 (1993) 547-577. Zbl0780.60079MR1230346
13. [13] J. Kuelbs, W. Li, M. Talagrand, Liminf results for Gaussian samples and Chung's functional LIL, Ann. Probab.22 (1994) 1879-1903. Zbl0849.60022MR1331209
14. [14] A. Lucas, Hausdorff–Besicovitch measure for random fractals of Chung's type, Math. Proc. Cambridge Philos. Soc.133 (2002) 487-513. Zbl1014.60029MR1919718
15. [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. Zbl0050.05803MR359031
16. [16] G. Shorack, J.A. Wellner, Empirical Processes with Applications to Statistics, John Wiley & Sons, 1986. Zbl1170.62365MR838963
17. [17] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahr. Verw. Gebiete3 (1964) 211-226. Zbl0132.12903MR175194
18. [18] Q. Wei, Functional modulus of continuity for Brownian motion in Hölder norm, Chinese Ann. Math. Ser. B22 (2001) 223-232. Zbl0974.60019MR1835402