Fast sets and points for fractional brownian motion

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1. [1] M.T. Barlow AND E. Perkins (1984). Levels at which every Brownian excursion is exceptional. Sém. Prob. XVIII, Lecture Notes in Math.1059, 1-28, Springer-Verlag, New York. Zbl0555.60050MR770945
2. [2] M. Csörgö AND P. Révész (1981). Strong Approximations in Probability and Statistics, Academic Press, New York. Zbl0539.60029MR666546
3. [3] P. Deheuvels AND M.A. Lifshits (1997). On the Hausdorff dimension of the set generated by exceptional oscillations of a Wiener process. Studia Sci. Math. Hung., 33, 75-110. Zbl0908.60012MR1454103
4. [4] P. Deheuvels AND D.M. Mason (1997). Random fractal functional laws of the iterated logarithm. (preprint) Zbl0916.60037MR1645150
5. [5] R.M. Dudley (1984). A Course on Empirical Processes. École d'Été de St. Flour 1982. Lecture Notes in Mathematics1097. Springer, Berlin. Zbl0554.60029MR876079
6. [6] J. Hawkes (1971). On the Hausdorff dimension of the range of a stable process with a Borel set. Z. Wahr. verw. Geb., 19, 90-102. Zbl0203.49903MR292165
7. [7] J. Hawkes (1981). Trees generated by a simple branching process. J. London Math. Soc., 24, 373-384. Zbl0468.60081MR631950
8. [8] J.-P. Kahane (1985). Some Random Series of Functions, second edition. Cambridge University Press, Cambridge. Zbl0571.60002MR833073
9. [9] R. Kaufman (1974). Large increments of Brownian Motion. Nagoya Math. J., 56, 139-145. Zbl0372.60114MR370796
10. [10] D. Khoshnevisan, Y. Peres AND Y. Xiao (1998). Limsup random fractals. In preparation. Zbl0949.60025
11. [11] N. Kôno (1977). The exact Hausdorff measure of irregularity points for a Brownian path. Z. Wahr. verw. Geb., 40, 257-282. Zbl0376.60081MR458564
12. [12] M. Ledoux AND M. Talagrand (1991). Probability in Banach Space, Isoperimetry and Processes, Springer-Verlag, Heidelberg-New York. Zbl0748.60004MR1102015
13. [13] P. Lévy (1937). Théorie de l'Addition des Variables Aléatoires. Gauthier-Villars, Paris. Zbl0016.17003MR586767JFM63.0490.04
14. [14] R. Lyons (1980). Random walks and percolation on trees. Ann. Prob., 18, 931-958. Zbl0714.60089
15. [15] M.B. Marcus (1968). Hölder conditions for Gaussian processes with stationary increments. Trans. Amer. Math. Soc., 134, 29-52. Zbl0186.50602MR230368
16. [16] M.B. Marcus AND J. Rosen (1992). Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes. J. Theoretical Prob., 5, 791-825. Zbl0761.60035MR1182681
17. [17] P. Matilla (1995). Geometry of Sets and Measures in Euclidean Spaces, Fractals and Rectifiability, Cambridge University Press, Cambridge. Zbl0819.28004
18. [18] S. Orey AND S.J. Taylor (1974). How often on a Brownian path does the law of the iterated logarithm fail?Proc. London Math. Soc., 28, 174-192. Zbl0292.60128MR359031
19. [19] Y. Peres (1996). Remarks on intersection-equivalence and capacity-equivalence. Ann. Inst. Henri Poincaré: Physique Théorique, 64, 339-347. Zbl0854.60077MR1400296
20. [20] E. Perkins AND S.J. Taylor (1988), Measuring close approaches on a Brownian path, Ann. Prob., 16, 1458-1480. Zbl0659.60113MR958197
21. [21] D. Revuz AND M. Yor (1994). Continuous Martingales and Brownian Motion, second edition. Springer, Berlin. Zbl0804.60001MR1303781
22. [22] G.R. Shorack AND J.A. Wellner (1986). Empirical Processes with Applications to Statistics. Wiley, New York. Zbl1170.62365MR838963
23. [23] S.J. Taylor (1966). Multiple points for the sample paths of the symmetric stable process, Z. Wahr. ver. Geb., 5, 247-64. Zbl0146.37905MR202193
24. [24] S.J. Taylor (1986). The measure theory of random fractals. Math. Proc. Camb. Phil. Soc., 100, 383-406. Zbl0622.60021MR857718