Analyse asymptotique des processus gaussiens stationnaires

Michel Weber

Annales de l'I.H.P. Probabilités et statistiques (1980)

  • Volume: 16, Issue: 2, page 117-176
  • ISSN: 0246-0203

How to cite

top

Weber, Michel. "Analyse asymptotique des processus gaussiens stationnaires." Annales de l'I.H.P. Probabilités et statistiques 16.2 (1980): 117-176. <http://eudml.org/doc/77141>.

@article{Weber1980,
author = {Weber, Michel},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {asymptotic behaviour of trajectories; stability of trajectories},
language = {fre},
number = {2},
pages = {117-176},
publisher = {Gauthier-Villars},
title = {Analyse asymptotique des processus gaussiens stationnaires},
url = {http://eudml.org/doc/77141},
volume = {16},
year = {1980},
}

TY - JOUR
AU - Weber, Michel
TI - Analyse asymptotique des processus gaussiens stationnaires
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1980
PB - Gauthier-Villars
VL - 16
IS - 2
SP - 117
EP - 176
LA - fre
KW - asymptotic behaviour of trajectories; stability of trajectories
UR - http://eudml.org/doc/77141
ER -

References

top
  1. [1] S.M. Berman, Limit theorems for the maximum term in stationary sequences. Ann. Math. Statist., t. 35, 1964, p. 502-516. Zbl0122.13503MR161365
  2. [2] S.M. Berman, Local time and sample function properties od stationary Gaussian processes. Trans. Amer. Math. Soc., t. 137, 1969, p. 277-299. Zbl0184.40801MR239652
  3. [3] P. Billingsley, Ergodic Theory. Ed. by F. B. Wright, Acad. Press, 1963, New York. MR158967
  4. [4] J.P. Conze, Systèmes topologiques et métriques en théorie ergodique. École d'Été de Probabilité de Saint-Flour (1974). Lect. Notes Math., t. 480, 1975, p. 100-187. Zbl0321.28010MR393421
  5. [5] K.L. Chung, P. Erdös et T. Sirao, On the Lipschitz's conditions for Brownian Motion. J. Math. Soc. Japan, vol. 11, n° 4, 1959, p. 263-274. Zbl0091.13301MR121873
  6. [6] X. Fernique, Régularité des trajectoires des fonctions aléatoires gaussiennes. École d'Été de Probabilité de Saint-Flour (1974). Lect. Notes Math., t. 480, 1975, p. 1-96. Zbl0331.60025MR413238
  7. [7] X. Fernique, Évaluation de processus gaussiens composés. Lect. Notes Math., t. 526, 1976, p. 67-83. Zbl0383.60037MR443054
  8. [8] X. Fernique, A paraître. 
  9. [9] N.C. Jain, K. Jogdeo et W.F. Stout, Upper and lower functions for Martingales and mixing Processes. Ann. of Prob., vol. 3, n° 1, 1975, p. 119-145. Zbl0301.60026MR368130
  10. [10] N. Kôno, Sur la minoration asymptotique et le caractère transitoire des trajectoires des fonctions aléatoires gaussiennes à valeurs dans Rd. Z. Wahrscheinlichkeitsth. verw. Gebiete, t. 33, 1975, p. 95-112. Zbl0322.60036MR397855
  11. [11] N. Kôno, Asymptotic behavior of sample functions of Gaussian random fields. J. Math. Kyoto Univ., t. 15 (3), 1975, p. 671-707. Zbl0339.60034MR458560
  12. [12] M.B. Marcus, Upper bounds for the asymptotic maxima of continuous Gaussian processes. Ann. Math. Stat., t. 43, 1972, p. 522-533. Zbl0241.60032MR388519
  13. [13] M.B. Marcus, Asymptotic Maxima of Continuous Gaussian Processes (II). Ann. of Prob., t. 2, 1974, p. 702-713. Zbl0304.60024MR370726
  14. [14] G. Maruyama, The harmonic analysis of stationary stochastic processes. Memoirs of the faculty of Sci. Kyusyu Univ., Ser. A, vol. IV, 1949, p. 45-106. Zbl0045.40602MR32127
  15. [15] J. Pickands, III, Maxima of stationary Gaussian processes. Z. Wahrscheinlichkeitsth. verw. Gebiete, t. 7, 1967, p. 190-223. Zbl0158.16702MR217866
  16. [16] J. Pickands, III, An iterated logarithm for the maximum in a stationary Gaussian sequence. Z. Wahrscheinlichkeitsth. verw. Gebiete, vol. 12, 1969, p. 344-353. Zbl0181.20703MR251776
  17. [17] C. Qualls et H. Watanabe, An asymptotic 0-1 behavior of Gaussian processes. Ann. Math. Stat., vol. 42, n° 6, 1971, p. 2027–2035. Zbl0239.60031MR307317
  18. [18] C. Qualls, H. Watanabe et G. Simmons, A note on a 0-1 law for stationary Gaussian processes. Inst. of Statis., Mimeo Series n° 793, 1972. 
  19. [19] C. Qualls et P.K. Pathak, A law of iterated logarithm for stationary Gaussian Processes. Trans. Amer. Math. Soc., vol. 18, 1973, p. 185-193. Zbl0273.60016MR321170
  20. [20] C. Qualls, The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion. Ann. of Prob., vol. 5, n° 5, 1977, p. 724- 739. Zbl0375.60035MR451369
  21. [21] H. Vishnu Hebbar , A law of the iterated logarithm for Extrem values from Gaussian Sequences. Z. Wahrscheinlichkeitsth. verw. Gebiete, vol. 48, 1979, p. 1-16. Zbl0387.60035MR533002
  22. [22] M. Weber, Classes supérieures de processus gaussiens. Z. Wahrscheinlichkeitsth. verw. Gebiete, vol. 42, 1978, p. 113-128. Zbl0374.60050MR494460
  23. [23] M. Weber, Tests intégraux pour certaines classes de processus gaussiens stationnaires à trajectoires continues. C. R. Acad. Sci. Paris, t. 287, série A, 1978, p. 969- 971. Zbl0391.60041MR520782

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.