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Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne

Catherine Bouton

Annales de l'I.H.P. Probabilités et statistiques (1988)

  • Volume: 24, Issue: 1, page 131-155
  • ISSN: 0246-0203

How to cite

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Bouton, Catherine. "Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne." Annales de l'I.H.P. Probabilités et statistiques 24.1 (1988): 131-155. <http://eudml.org/doc/77316>.

@article{Bouton1988,
author = {Bouton, Catherine},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic approximation algorithms; asymptotic behaviour; Gaussian diffusions; transition kernels; mixing properties},
language = {fre},
number = {1},
pages = {131-155},
publisher = {Gauthier-Villars},
title = {Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne},
url = {http://eudml.org/doc/77316},
volume = {24},
year = {1988},
}

TY - JOUR
AU - Bouton, Catherine
TI - Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1988
PB - Gauthier-Villars
VL - 24
IS - 1
SP - 131
EP - 155
LA - fre
KW - stochastic approximation algorithms; asymptotic behaviour; Gaussian diffusions; transition kernels; mixing properties
UR - http://eudml.org/doc/77316
ER -

References

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  1. [1] A. Benveniste, Introduction à la méthode de l'équation différentielle moyenne pour l'étude des algorithmes récursifs, exemples, C.N.R.S., Outils et Modèles mathématiques pour l'Automatique, l'Analyse des Systèmes, et le Traitement du Signal, vol. 1, 1981. Zbl0463.93067
  2. [2] P. Billingsley, Convergence of Probability Measures, Wiley, 1968. Zbl0172.21201MR233396
  3. [3] C. Bouton, Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne, Thèse de 3e cycle, éditée par l'École Polytechnique. Zbl0643.60038
  4. [4] M.I. Freidlin et A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer, 1984. Zbl0522.60055MR722136
  5. [5] E.G. Gladyshev, On Stochastic Approximation, Theory of Probability and its Applications, vol. 10, p. 275-278. 
  6. [6] S. Geman, Approximate Solution of Random Equations, Bharucha-Reid, 1979. Zbl0466.62076
  7. [7] R.Z. Khas'minsky, On Stochastic Processes Defined by Differential Equations with a Small Parameter, Theory Prob. Appl., vol. II, 1966, p. 211-222. Zbl0168.16002
  8. [8] H.J. Kushner et H. Huang, Rates of convergence for stochastic approximation type algorithms, S.I.A.M. J. Control, vol. 17, n° 5, 1979. Zbl0418.93093MR540841
  9. [9] H.J. Kushner, A Martingale Method for the Convergence of a Sequence of Processes to a Jump-Diffusion Process, Z. W., vol. 53, 1980, p. 209-219. Zbl0417.60009MR580914
  10. [10] H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, M.I.T. Press, Cambridge, 1984. Zbl0551.60056MR741469
  11. [11] L. Ljung et T. Soderström, Theory and Practice of Recursive Identification, M.I.T. Press, 1983. Zbl0548.93075MR719192
  12. [12] L. Ljung, Analysis of Recursive Stochastic Algorithms, I.E.E.E. Trans. on Autom. Control, vol. AC 22, n° 4, 1977. Zbl0362.93031MR465458
  13. [13] M. Metivier et P. Priouret, Théorèmes de convergence presque sûre pour une classe d'algorithmes à pas décroissants, Probability Theory (à paraître). Zbl0588.62153
  14. [14] M. Metivier et P. Priouret, Convergence avec probabilité (1-∈) d'algorithmes stochastiques et application à l'égaliseur aveugle, Ann. des Télécommunications, t. 41, n° 5-6, 1986. Zbl0607.62097
  15. [15] M. Metivier et P. Priouret, Application of a Kushner and Clark Lemma to General Classes of Stochastic Algorithms, I.E.E.E. Trans. Inf. Theory, vol. IT-30, 1984, p. 140- 150. Zbl0546.62056MR807052
  16. [16] G.C. Papanicolaou et N. Kolher, Asymptotic Theory of Mixing Stochastic Ordinary Differential Equations, Comm. Pure Appl. Math., vol. 27, 1974, p. 641-668. Zbl0288.60056MR368142
  17. [17] Sacks, Asymptotic Distribution of Stochastic Approximation Procedures, Ann. Math. Stat., vol. 29, 1958, p. 373-405. Zbl0229.62010MR98427
  18. [18] D.W. Strook et S.R.S. Varadhan, Multidimensionnal Diffusion Processus, Springer-Verlag, Berlin, 1979. 

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