Tail probabilities of gaussian suprema and Laplace transform
Lifshits, M. A.
Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994), p. 163-179 / Harvested from Numdam
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Publié le : 1994-01-01
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     author = {Lifshits, M. A.},
     title = {Tail probabilities of gaussian suprema and Laplace transform},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {30},
     year = {1994},
     pages = {163-179},
     mrnumber = {1276995},
     zbl = {0796.60029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1994__30_2_163_0}
}

Lifshits, M. A. Tail probabilities of gaussian suprema and Laplace transform. Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994) pp. 163-179. http://gdmltest.u-ga.fr/item/AIHPB_1994__30_2_163_0/

[1] R.J. Adler, An Introduction to Continuity, Extrema and Related Topics for General Gaussian Processes. Lecture Notes of Inst. Math. Stat., Vol. 12, IMS, Hayword, 1990. | MR 1088478 | Zbl 0747.60039

[2] V.A. Dmitrowskii, On the Integrability of the Maximum and Conditions of Continuity and Local Properties of Gaussian Fields. In Grigelionis B. (Ed.), Probability Theory and Mathematical Statistics, Proceedings 5-th Vilnius Conference, VSP/Mokslas, Vilnius, Vol. 1, 1990, pp. 271-284. | Zbl 0726.60052

[3] V. Dobrič, M.B. Marcus and M. Weber, The Distribution of Large Values of the Supremum of a Gaussian Process, Astérisque, Vol. 157-158, 1988, pp. 95-127. | MR 976215 | Zbl 0659.60061

[4] R.M. Dudley, Sample Functions of Gaussian Processes, Ann. Probab., Vol. 1, 1973, pp. 66-103. | MR 346884 | Zbl 0261.60033

[5] A. Ehrhard, Symetrisation dans l'espace de Gauss, Math. Scand., Vol. 53, 1983, pp. 281-301. | MR 745081 | Zbl 0542.60003

[6] X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, Lect. Notes Math., Vol. 480, 1975, pp. 2-187. | MR 413238 | Zbl 0331.60025

[7] K. Ito and M. Nisio, On the Oscillation Function of Gaussian Process, Math. Scand., Vol. 22, 1968, pp. 209-223. | MR 243597 | Zbl 0231.60027

[8] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. | MR 1102015 | Zbl 0748.60004

[9] M.A. Lifshits, The Calculation of Exact Asymptotic Behavior of Some Gaussian Large Deviations (in Russian). Zapiski Nauchnykh Seminarov LOMI, Vol. 184, 1991, pp. 189-199. | MR 1098699 | Zbl 0760.60026

[10] M.A. Lifshits, Unexpected Limit Behavior of the Gaussian Tail Probabilities. In Prokhorov Ju. (Ed.), New Trends in Probability and Statistics, VSP/Mokslas, Vilnius, 1991. | MR 1200919 | Zbl 0768.60007

[11] M.A. Lifshits, Gaussian Large Deviations of a Smooth Seminorm. In: Shiryaev A. N. (Ed.), Probability Theory and Mathem. Statistics (Proc. Sixth USSR-Japan Symposium), 1992, World Scientific, Singapore, pp. 193-201. | MR 1212124 | Zbl 0830.60005

[12] W. Linde, Gaussian Measure of the Large Balls in lp, Ann. Probab., Vol. 19, 1991, pp. 1264-1280. | MR 1112415 | Zbl 0736.60004

[13] W. Linde, Gaussian Measure of the Large Balls in R". In: Cambanis S. (Ed.), Stable Processes and Related Topics, 1991, Birkhauser, Boston, pp. 1-25. | Zbl 0727.60011

[14] M. Talagrand, Sur l'intégrabilité des vecteurs gaussiens, Z. Wahrsch. verw. Gebiete, Bd. 68, No. 1, 1984, s. 1-8. | MR 767440 | Zbl 0529.60034

[15] M. Talagrand, Small Tails for the Supremum of a Gaussian Process, Ann. Inst. H. Poincaré, Vol. 24, No. 2, 1988, pp. 307-315. | Numdam | MR 953122 | Zbl 0641.60044

[16] V.M. Zolotarev, Concerning a Certain Probability Problem, Theory Probab. Appl., Vol. 6, 1991, pp. 201-204. | Zbl 0109.36404