Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations

E. Eweda; O. Macchi

Annales de l'I.H.P. Probabilités et statistiques (1983)

  • Volume: 19, Issue: 3, page 235-255
  • ISSN: 0246-0203

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Eweda, E., and Macchi, O.. "Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations." Annales de l'I.H.P. Probabilités et statistiques 19.3 (1983): 235-255. <http://eudml.org/doc/77211>.

@article{Eweda1983,
author = {Eweda, E., Macchi, O.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {almost-sure convergence; correlated observations; quadratic mean convergence; stochastic gradient algorithm; finite memory; finite moments},
language = {eng},
number = {3},
pages = {235-255},
publisher = {Gauthier-Villars},
title = {Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations},
url = {http://eudml.org/doc/77211},
volume = {19},
year = {1983},
}

TY - JOUR
AU - Eweda, E.
AU - Macchi, O.
TI - Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1983
PB - Gauthier-Villars
VL - 19
IS - 3
SP - 235
EP - 255
LA - eng
KW - almost-sure convergence; correlated observations; quadratic mean convergence; stochastic gradient algorithm; finite memory; finite moments
UR - http://eudml.org/doc/77211
ER -

References

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  1. [1] H. Robbins, S. Monro, « A Stochastic Approximation Method », The Annals of Mathematical Statistics, t. 22, 1951, p. 400-407. Zbl0054.05901MR42668
  2. [2] L. Schmetterer, « Stochastic Approximation », Proc. of the Fourth Berkeley Symp. on Math. Stat. and Proba., p. 587-609. Zbl0104.12403MR137268
  3. [3] D. Sakrison, « Stochastic Approximation, a Recursive Method for Solving Regression Problems », Adv. in Comm. Systems, A. V. Balakrishnan Éditeur, Acad. Press, 1966, p. 51-106. 
  4. [4] C. Macchi, Itération stochastique et Traitements numériques adaptatifs, Thèse d'État, Paris, 1972. 
  5. [5] B. Widrow, J.M. Mccool, M.G. Larimore, C.R. Johnson, « Stationary learning characteristics of the LMS adaptive filter »Proc. IEEE, t. 64, n° 8, 1976, p. 1151-1162. MR421814
  6. [6] O. Macchi, « Résolution adaptative de l'équation de Wiener-Hopf. Cas d'un canal de données affecté de gigue », Ann. Inst. Henri Poincaré, t. 14, n° 3, 1978, p. 355-377. Zbl0378.62073MR508936
  7. [7] H.J. Kushner, D.S. Clark, « Stochastic approximation methods for constrained and unconstrained systems », Appl. Math. Sci. Series, n° 26, Springer-Verlag, Berlin, 1978, ch. 1. Zbl0381.60004MR499560
  8. [8] L. Ljung, « Analysis of a recursive stochastic algorithm », IEEE Trans. on Automatic Control, t. AC 22, 1977, p. 551-575. Zbl0362.93031MR465458
  9. [9] D.C. Farden, « Stochastic Approximation with Correlated Data », IEEE Trans. on Information Theory, t. IT 27, n° 1, 1981, p. 105-113. Zbl0458.62072MR605941
  10. [10] E. Eweda, O. Macchi, « Convergence of an adaptive linear estimation algorithm », IEEE Trans. on Automatic Control, t. AC 28, n° 10, octobre 1983. Zbl0501.93064
  11. [11] O. Macchi, E. Eweda, « Second order convergence analysis of stochastic adaptive linear filtering ». IEEE Trans. on Automatic Control, t. 28, n° 1, janvier 1983, p. 76-85. Zbl0501.93064MR711090
  12. [12] E. Eweda, Egalisation adaptative d'un canal filtrant non stationnaire. Thèse Ingénieur-Docteur, Orsay, 19 mars 1980. 
  13. [13] E. Eweda, O. Macchi, « Poursuite adaptative du filtrage optimal non stationnaire ». C. R. Acad. Sci., t. 293, série I, 1981, p. 497-500. Zbl0478.60050MR646875
  14. [14] H. Cramer and M.R. Leadbetter, Stationary and Related Stochastic Processes. New York: Wiley, 1967. Zbl0162.21102MR217860

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