@article{AIHPB_2006__42_3_373_0, 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}, volume = {42}, number = {3}, year = {2006}, doi = {10.1016/j.anihpb.2005.06.001}, zbl = {05024241}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2005.06.001/} }
TY - JOUR AU - Lucas, Alain AU - Thilly, Emmanuel TI - Hausdorff-Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2006 SP - 373 EP - 392 VL - 42 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2005.06.001/ DO - 10.1016/j.anihpb.2005.06.001 LA - en ID - AIHPB_2006__42_3_373_0 ER -
%0 Journal Article %A Lucas, Alain %A Thilly, Emmanuel %T Hausdorff-Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms %J Annales de l'I.H.P. Probabilités et statistiques %D 2006 %P 373-392 %V 42 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2005.06.001/ %R 10.1016/j.anihpb.2005.06.001 %G en %F AIHPB_2006__42_3_373_0
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] On the functional form of Lévy's modulus of continuity for Brownian motion, Z. Wahr. Verw. Gebiete 69 (1985) 567-579. | MR | Zbl
,[2] 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] How small are the increments of a Wiener process?, Stochastic Process. Appl. 8 (1979) 119-129. | MR | Zbl
, ,[5] 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] Random fractals generated by oscillations processes with stationary and independent increments, in: , , (Eds.), Probability in Banach Spaces, vol. 9, 1994, pp. 73-90. | MR | Zbl
, ,[7] Random fractal functional laws of the iterated logarithm, Studia Sci. Math. Hungar. 34 (1997) 89-106. | MR | Zbl
, ,[8] On the fractal nature of empirical increments, Ann. Probab. 23 (1995) 355-387. | MR | Zbl
, ,[9] Chung's law and Csáki function, J. Theoret. Probab. 12 (1999) 399-420. | MR | Zbl
, ,[10] Fractal Geometry, Mathematical Foundations and Applications, Wiley, New York, 1990. | MR | Zbl
,[11] Limsup random fractals, Electron. J. Probab. 5 (2000) 1-24. | MR | Zbl
, , ,[12] Small ball estimates for Brownian motion and the Brownian sheet, J. Theoret. Probab. 6 (1993) 547-577. | MR | Zbl
, ,[13] Liminf results for Gaussian samples and Chung's functional LIL, Ann. Probab. 22 (1994) 1879-1903. | MR | Zbl
, , ,[14] Hausdorff-Besicovitch measure for random fractals of Chung's type, Math. Proc. Cambridge Philos. Soc. 133 (2002) 487-513. | MR | Zbl
,[15] 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] Empirical Processes with Applications to Statistics, John Wiley & Sons, 1986. | MR | Zbl
, ,[17] An invariance principle for the law of the iterated logarithm, Z. Wahr. Verw. Gebiete 3 (1964) 211-226. | MR | Zbl
,[18] Functional modulus of continuity for Brownian motion in Hölder norm, Chinese Ann. Math. Ser. B 22 (2001) 223-232. | MR | Zbl
,Cited by Sources: