Tail probabilities of gaussian suprema and Laplace transform

M. A. Lifshits

Annales de l'I.H.P. Probabilités et statistiques (1994)

  • Volume: 30, Issue: 2, page 163-179
  • ISSN: 0246-0203

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Lifshits, M. A.. "Tail probabilities of gaussian suprema and Laplace transform." Annales de l'I.H.P. Probabilités et statistiques 30.2 (1994): 163-179. <http://eudml.org/doc/77477>.

@article{Lifshits1994,
author = {Lifshits, M. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Gaussian random function; Laplace transform; Gaussian measure; large deviations},
language = {eng},
number = {2},
pages = {163-179},
publisher = {Gauthier-Villars},
title = {Tail probabilities of gaussian suprema and Laplace transform},
url = {http://eudml.org/doc/77477},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Lifshits, M. A.
TI - Tail probabilities of gaussian suprema and Laplace transform
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 2
SP - 163
EP - 179
LA - eng
KW - Gaussian random function; Laplace transform; Gaussian measure; large deviations
UR - http://eudml.org/doc/77477
ER -

References

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  1. [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. Zbl0747.60039MR1088478
  2. [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. Zbl0726.60052
  3. [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. Zbl0659.60061MR976215
  4. [4] R.M. Dudley, Sample Functions of Gaussian Processes, Ann. Probab., Vol. 1, 1973, pp. 66-103. Zbl0261.60033MR346884
  5. [5] A. Ehrhard, Symetrisation dans l'espace de Gauss, Math. Scand., Vol. 53, 1983, pp. 281-301. Zbl0542.60003MR745081
  6. [6] X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, Lect. Notes Math., Vol. 480, 1975, pp. 2-187. Zbl0331.60025MR413238
  7. [7] K. Ito and M. Nisio, On the Oscillation Function of Gaussian Process, Math. Scand., Vol. 22, 1968, pp. 209-223. Zbl0231.60027MR243597
  8. [8] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. Zbl0748.60004MR1102015
  9. [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. Zbl0760.60026MR1098699
  10. [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. Zbl0768.60007MR1200919
  11. [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. Zbl0830.60005MR1212124
  12. [12] W. Linde, Gaussian Measure of the Large Balls in lp, Ann. Probab., Vol. 19, 1991, pp. 1264-1280. Zbl0736.60004MR1112415
  13. [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. Zbl0727.60011
  14. [14] M. Talagrand, Sur l'intégrabilité des vecteurs gaussiens, Z. Wahrsch. verw. Gebiete, Bd.68, No. 1, 1984, s. 1-8. Zbl0529.60034MR767440
  15. [15] M. Talagrand, Small Tails for the Supremum of a Gaussian Process, Ann. Inst. H. Poincaré, Vol. 24, No. 2, 1988, pp. 307-315. Zbl0641.60044MR953122
  16. [16] V.M. Zolotarev, Concerning a Certain Probability Problem, Theory Probab. Appl., Vol. 6, 1991, pp. 201-204. Zbl0109.36404

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