Convergence presque sûre de processus d'approximation stochastique dynamique

Jean-Marie Monnez

Statistique et analyse des données (1989)

  • Volume: 14, Issue: 2, page 55-79
  • ISSN: 0750-7364

How to cite

top

Monnez, Jean-Marie. "Convergence presque sûre de processus d'approximation stochastique dynamique." Statistique et analyse des données 14.2 (1989): 55-79. <http://eudml.org/doc/108981>.

@article{Monnez1989,
author = {Monnez, Jean-Marie},
journal = {Statistique et analyse des données},
language = {fre},
number = {2},
pages = {55-79},
publisher = {Association pour la statistique et ses illustrations},
title = {Convergence presque sûre de processus d'approximation stochastique dynamique},
url = {http://eudml.org/doc/108981},
volume = {14},
year = {1989},
}

TY - JOUR
AU - Monnez, Jean-Marie
TI - Convergence presque sûre de processus d'approximation stochastique dynamique
JO - Statistique et analyse des données
PY - 1989
PB - Association pour la statistique et ses illustrations
VL - 14
IS - 2
SP - 55
EP - 79
LA - fre
UR - http://eudml.org/doc/108981
ER -

References

top
  1. [1] Albert, A.E., Gardner, L.A., Stochastic Approximation and Nonlinear Regression, Research Monograph 42, M.I.T. Press, Cambridge, Massachusetts, 1967. Zbl0162.21502MR224217
  2. [2] Assili, O., Régression séquentielle par approximation stochastique, Thèse de Doctorat de troisième cycle, Université de Nancy 1, 1985. 
  3. [3] Bennar, A., Approximation stochastique : convergence dans le cas de plusieurs solutions et étude de modèles de corrélations, Thèse de Doctorat de troisième cycle, Université de Nancy 1, 1985. 
  4. [4] Benveniste, A., Metivier, M., Priouret, P., Algorithmes adaptatifs et approximations stochastiques, Théorie et applications, Masson, 1987. Zbl0639.93002
  5. [5] Blum, J.R., "Multidimensional Stochastic Approximation Methods", AMS, 1954, Vol. 25, pp. 737-744. Zbl0056.38305MR65092
  6. [6] Dupac, V., "A Dynamical Stochastic Approximation Method", AMS, 1965, Vol. 36, pp. 1695-1702. Zbl0137.36504MR193724
  7. [7] Dupac, V., "Stochastic Approximations in the Presence of Trend", Czechoslovak Math. J., 1966, Vol. 16 (91), pp. 454-461. Zbl0218.62097MR199921
  8. [8] Gladyshev, E.G., "On Stochastic Approximation", Theory of Probability and its Applications, 1965, Vol. 10, pp. 275-278. 
  9. [9] I.E.E.E. TRANSACTIONS ON INFORMATION THEORY, 1984, Vol. IT-30, n°2. 
  10. [10] Kiefer, J., Wolfowitz, J., "Stochastic Estimation of the Maximum of a Regression Function", AMS, 1952, Vol. 23, pp. 462-466. Zbl0049.36601MR50243
  11. [11] Ljung, L., Soderstrom, T., Theory and Practice of Recursive Identification, M.I.T. Press, 1983. Zbl0548.93075MR719192
  12. [12] Monnez, J.M., Etude d'un processus général multidimensionnel d'approximation stochastique sous contraintes convexes. Applications à l'estimation statistique, Thèse de Doctorat ès Sciences Mathématiques, Université de Nancy I, 1982. 
  13. [13] Nevel'son, M.B., Has'minskii, R.Z., Stochastic Approximation and Recursive Estimation, Translation of Mathematical Monographs, Vol. 47, American Mathematical Society, Providence, Rhode Island, 1973. Zbl0355.62075MR423714
  14. [14] Robbins, H., Monro, S., "A Stochastic Approximation Method", AMS, 1951, Vol. 22, pp. 400-407. Zbl0054.05901MR42668
  15. [15] Robbins, H., Siegmund, D., "A Convergence Theorem for Nonnegative almost Supermartingales and some Applications", Optimizing Methods in Statistics, edited by J.S. Rustagi, Academic Press, New York, 1971, pp. 233-257. Zbl0286.60025MR343355
  16. [16] Ruppert, D., "A New Dynamic Stochastic Approximation Procedure", AS, 1979, Vol. 7, n° 6, pp. 1179-1195. Zbl0427.62059MR550143
  17. [17] Uosaki, K., "Some Generalizations of Dynamic Stochastic Approximation Processes", AS, 1974, Vol. 2, n° 5, pp. 1042-1048. Zbl0288.62038MR359214
  18. [18] Uosaki, K., "State Estimation Scheme for Nonlinear Dynamical Systems Based on the Stochastic Approximation", Information Sciences, 1975, Vol. 9, pp. 133-149. Zbl0319.93052MR386826
  19. [19] Uosaki, K., "An Asymptotically more Efficient Nonlinear State Estimation Scheme Based on the Stochastic Approximation", Int. J. Systems Sci., 1977, Vol. 8, n° 9, pp. 971-983. Zbl0362.93022MR456847
  20. [20] Venter, J.H., "On Dvoretzky Stochastic Approximation Theorems", AMS, 1966, Vol. 37, pp. 1534-1544. Zbl0146.39505MR203786
  21. [21] Wasan, M.T., Stochastic Approximation, Cambridge Tracts in Mathematics and Mathematical Physics, n° 58, Cambridge University Press, 1969. Zbl0293.62026MR247712

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.