Chung-type functional laws of the iterated logarithm for tail empirical processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 5, pp. 583-616.
@article{AIHPB_2000__36_5_583_0,
     author = {Deheuvels, Paul},
     title = {Chung-type functional laws of the iterated logarithm for tail empirical processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {583--616},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {5},
     year = {2000},
     mrnumber = {1792657},
     zbl = {0973.60027},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2000__36_5_583_0/}
}
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Deheuvels, Paul. Chung-type functional laws of the iterated logarithm for tail empirical processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 5, pp. 583-616. http://archive.numdam.org/item/AIHPB_2000__36_5_583_0/

[1] De Acosta A., Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm, Ann. Probab. 11 (1983) 78-101. | MR | Zbl

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

[3] Adler R.J., An Introduction to Continuity, Extrema and Related Topics for General Gaussian Processes, IMS, Hayward, CA, 1990. | MR | Zbl

[4] Ash R.A., Gardner M.F., Topics in Stochastic Processes, Academic Press, New York, 1975. | MR | Zbl

[5] Berthet P., On the rate of clustering to the Strassen set for increments of the uniform empirical process, J. Theoret. Probab. 10 (1997) 557-579. | MR | Zbl

[6] Borell C., A note on Gaussian measures which agree on balls, Ann. Inst. Henri Poincaré, Probab. Statist. 13 (1977) 231-238. | Numdam | MR | Zbl

[7] Borovkov A.A., Mogulskii A.A., On probabilities of small deviations for stochastic processes, Siberian Adv. Math. 1 (1991) 39-63. | MR | Zbl

[8] Cameron R.H., Martin W.T., Evaluations of various Wiener integrals by use of certain Sturm-Liouville differential equations, Bull. Amer. Math. Soc. 51 (1945) 73-90. | MR | Zbl

[9] Castelle L., Laurent-Bonvalot L., Strong approximations of bivariate uniform empirical processes, Ann. Inst. Henri Poincaré, Probab. Statist. 34 (1998) 425-480. | Numdam | MR | Zbl

[10] Chung K.L., On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948) 205-233. | MR | Zbl

[11] Csáki E., A relation between Chung's and Strassen's law of the iterated logarithm, Z. Wahrsch. Verw. Gebiete 54 (1980) 287-301. | MR | Zbl

[12] Csáki E., A lim inf result in Strassen's law of the iterated logarithm, Colloq. Math. Soc. János Bolyai 57 (1989) 83-93. | MR | Zbl

[13] Csörgö M., Mason D.M., On the asymptotic distribution of weighted uniform empirical and quantile processes in the middle and on the tails, Stochastic Process. Appl. 21 (1985) 119-132. | MR | Zbl

[14] Csörgö M., Révész P., How small are the increments of a Wiener process?, Stochastic Process. Appl. 8 (1978) 119-129. | MR | Zbl

[15] M. Csörgö M., Révész P., Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. | MR | Zbl

[16] Deheuvels P., Strong laws for local quantile processes, Ann. Probab. 25 (1997) 2007-2054. | MR | Zbl

[17] Deheuvels P., Lifshits M.A., Necessary and sufficient conditions for the Strassen law of the iterated logarithm in nonuniform topologies, Ann. Probab. 22 (1994) 1838-1856. | MR | Zbl

[18] Deheuvels P., Mason D.M., Nonstandard functional laws of the iterated logarithm for tail empirical and quantile processes, Ann. Probab. 18 (1990) 1693-1722. | MR | Zbl

[19] Deheuvels P., Mason D.M., Random fractal functional laws of the iterated logarithm, Studia Sci. Math. Hungar. 34 (1998) 89-106. | MR | Zbl

[20] Goodman V., Kuelbs J., Rates of clustering for some Gaussian self-similar processes, Probab. Theory Related Fields 88 (1991) 47-75. | MR | Zbl

[21] Grill K., A lim inf result in Strassen's law of the iterated logarithm, Probab. Theory Related Fields 89 (1991) 149-157. | MR | Zbl

[22] Itô K., Mckean H.P. Jr., Diffusion Processes and their Sample Paths, Springer, Berlin, 1965. | MR | Zbl

[23] Kuo H.H., Gaussian Measures in Banach Spaces, Lectures Notes in Math., Vol. 463, Springer, Berlin, 1975. | MR | Zbl

[24] Kuelbs J., The law of the iterated logarithm in C[0, 1], Z. Wahrsch. Verw. Gebiete 33 (1976) 221-235. | MR | Zbl

[25] Kuelbs J., A strong convergence theorem for Banach space valued random variables, Ann. Probab. 4 (1976) 744-771. | MR | Zbl

[26] Kuelbs J., Li W.V., Talagrand M., Lim inf results for Gaussian samples and Chung's functional LIL, Ann. Probab. 22 (1994) 1789-1903. | MR | Zbl

[27] Ledoux M., Talagrand M., Probability in Banach Spaces, Springer, Berlin, 1991. | MR | Zbl

[28] Lifshits M.A., Gaussian Random Functions, Kluwer, Dordrecht, 1995. | MR | Zbl

[29] Mason D.M., A strong invariance theorem for the tail empirical process, Ann. Inst. Henri Poincaré, Probab. Statist. 24 (1988) 491-506. | Numdam | MR | Zbl

[30] Mason D.M., Van Zwet W.R., A refinement of the KMT inequality for the uniform empirical process, Ann. Probab. 15 (1987) 871-884. | MR | Zbl

[31] Mogulskii A.A., Small deviations in the space of trajectories, Teor. Veroiatnost. i Primenen. 19 (1974) 726-736 (in Russian). | MR | Zbl

[32] Mogulskii A.A., On the law of the iterated logarithm in Chung form for functional spaces, Teor. Veroiatnost. i Primenen. 24 (1979) 399-407 (in Russian). | MR | Zbl

[33] Mueller C., A unification of Strassen's law and Lévy's modulus of continuity, Z. Wahrsch. Verw. Gebiete 56 (1981) 163-179. | MR | Zbl

[34] Nagaev S.V., On asymptotics of the Wiener measure on a narrow strip, Teor. Veroiatnost. i Primenen. 26 (1981) 630 (in Russian).

[35] Révész P., A generalization of Strassen's functional law of iterated logarithm, Z. Wahrsch. Verw. Gebiete 50 (1979) 257-264. | MR | Zbl

[36] Shorack G.R., Wellner J.A., Empirical Processes with Applications to Statistics, Wiley, New York, 1986. | MR | Zbl

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