Voir la notice de l'article provenant de la source Math-Net.Ru
@article{THSP_2007_13_2_a10,
author = {{\CYRT}{\cyro}{\cyrm}{\cyra}{\cyrs} {\CYRS}{\cyri}{\cyrm}{\cyro}{\cyrn}},
title = {{\CYRM}{\cyra}{\cyrl}{\cyrery}{\cyre} {\cyru}{\cyrk}{\cyrl}{\cyro}{\cyrn}{\cyre}{\cyrn}{\cyri}{\cyrya} {\cyrn}{\cyre}{\cyrg}{\cyra}{\cyru}{\cyrs}{\cyrs}{\cyro}{\cyrv}{\cyrs}{\cyrk}{\cyri}{\cyrh} {\cyrp}{\cyrr}{\cyro}{\cyrc}{\cyre}{\cyrs}{\cyrs}{\cyro}{\cyrv}},
journal = {Teori\^a slu\v{c}ajnyh processov},
pages = {272--280},
publisher = {mathdoc},
volume = {13},
number = {2},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a10/}
}
Томас Симон. Малые уклонения негауссовских процессов. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 272-280. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a10/
[1] A. de Acosta, “Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm”, Ann.Probab., 11 (1983), 78–101
[2] F. Aurzada, Metric entropy and the small deviation problem for stable processes, 2006
[3] F. Aurzada, T. Simon, “Small deviations for stable convolution process”, ESAIM Probability Statistics, 2006 (to appear)
[4] P. Baldi, B. Roynette, “Some exact equivalents for the Brownian motion in Hölder semi-norm”, Prob.Th.Rel.Fields, 93:4 (1992), 457-–484
[5] J. Bertoin, “On the first exit time of a completely asymmetric stable process from a finite interval”, Bull.London Math.Soc., 28:5 (1996), 514-–520
[6] J. Bretagnolle, “$p$-variation de fonctions aléatoires”, Sem.Probab., 6 (1972), 51-71
[7] K. L. Chung, “On the maximum partial sums of sequence of independent random variables”, Trans.Am.Math.Soc., 64 (1948), 205-–233
[8] X. Chen, J. Kuelbs, W. V. Li, “A functional LIL for symmetric stable processes”, Ann.Probab., 28:1 (2000), 258-–276
[9] C. Donati-Martin, S. Song, M. Yor, “Symmetric stable processes, Fubini's theorem, and some extensions of the Ciesielski-Taylor identities in law”, Stochastics Rep., 50:1-2 (1994), 1-–33
[10] M. D. Donsker, S. R. S. Varadhan, “On laws of the iterated logarithm for local times”, Commun. Pure Appl. Math., 30 (1977), 707–753
[11] P. E. Greenwood, “The variation of a stable path is stable”, Z. Wahrscheinlichkeitstheor. Verw. Geb., 14 (1969), 140–148
[12] K. Grill, “Exact rate of convergence in Strassen’s law of the iterated logarithm”, J. Theor. Probab., 5:1 (1992), 197–204
[13] W. V. Li., “A Gaussian correlation inequality and its applications to small ball probabilities”, Electron. Commun. Probab., 4 (1999), 111–118
[14] W. V. Li, W. Linde, “Approximation, metric entropy and small ball estimates for Gaussian measures”, Ann. Probab., 27:3 (1999), 1556–1578
[15] W. V. Li, W. Linde, “Small deviations of stable processes via metric entropy metric entropy”, J. Theoret. Probab., 17:1 (2004), 261–284
[16] W. V. Li, Q.-M. Shao, “Gaussian Processes: Inequalities, Small Ball Probabilities and Applications”, Stochastic processes: Theory and methods, Handbook of Statistics, 19 (2001), 533–597
[17] W. Linde, Z. Shi, “Evaluating the small deviation probabilities for subordinated Lévy processes”, Stoch. Proc. Appl., 113:2 (2004), 273–288
[18] M. A. Lifshits, T. Simon, “Small deviations for fractional stable processes”, Ann. Inst. H. Poincaré Probab. Statistiques, 41:4 (2005), 725–752
[19] A. A. Mogulskii, “Malye ukloneniya v prostranstve traektorii”, Teop. Bep.Prim., 19 (1974), 726–736
[20] L. N’Guyen Ngoc., Dis., Universitet,Parizh 6, 2003
[21] J. Rushton, A functional law of the iterated logarithm for stable processes and related invariance results, Preprint, 2005
[22] Z. Shi, “Lower tails of quadratic functionals of symmetric stable processes”, 1999 (to appear)
[23] E. Yu. Shmileva, “Small ball probabilities for a centered Poisson process of high intensity”, J. Math. Sci., 128:1 (2005), 2656–2668
[24] Z. Sidk, “On multivariate normal probabilities of rectangles: Their dependence on correlations”, Ann. Math. Statist., 39 (1968), 1425–1434
[25] T. Simon, “Sur les petites déviations d’un processus de Lévy”, Potential Anal., 14:2 (2001), 155–173
[26] T. Simon, “Small deviations in $p$-variation norm for multidimensional Lévy processes”, J. Math. Kyoto Univ., 43:3 (2003 \), 943–986
[27] T. Simon, Small ball estimates in $p$-variation for stable processes, 17:4 (2004), 1013–1036
[28] S. J. Taylor., “Sample path properties of a transient stable process”, J. Math. Mech., 16 (1967), 1229–1246