Applications of a Kushner and Clark Lemma to General Classes of Stochastic Algorithms

IEEE Transactions on Information Theory

Volumn 30, Issue 2, 1984, Pages 140-151

  Metivier, Michel ^a   Priouret, Pierre ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE FILTERING;

SIGNAL FILTERING AND PREDICTION;

EID: 0021385812     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1984.1056894     Document Type: Article

References (13)

1. D. P. Deveritskii and A. L. Fradkov, “Two models for analysing the dynamics of adaptation algorithms, ” Automatika i Telemekhanika, no. 1, pp. 66–75, Jan. 1974.
2. E. Eweda and 0. Macchi, “Convergence of an adaptative linear estimation algorithm, ” IEEE Trans. Automat. Contr., vol. AC-29, no. 2, pp. 119–127, Feb. 1984.
3. —, “Quadratic mean and almost sure convergence of unbounded stochastic approximation algorithms with correlated observations, ” Ann. de l'Inst. Henri Poincaré, vol. 19, no. 1, Jan. 1983.
4. H. Kushner and D. S. Clark, “Stochastic approximation for constrained and unconstrained systems, ” Appl. Math. Sci., vol. 26, Berlin-Heidelberg-New York, 1978.
5. H. Kushner, “Stochastic approximation with discontinuous dynamics and state dependent noise, ” J. Math. Anal. and Appl., vol. 82, pp. 527-542, 1981.
6. H. Kushner and A. Shwartz, “Convergence of stochastic approximations with state dependent noise under weak conditions, ” C. D.C. IEEE, 517–521, 1982.
7. E. G. Gladysev, “On stochastic approximation, ” Teor. Verojatnost. i. Primenen, vol. 10, pp. 297-300, 1965, and Theory Prob. Appl., vol. 10, pp. 275–278, 1965.
8. L. Ljung, “Analysis of recursive stochastic algorithms, ” IEEE Trans. Automat. Control, vol. AC-22, no. 2, pp. 551–575, 1977.
9. [9] M. Metivier, Semimartingales. Berlin: W. de 1982.
10. M. B. Nevelson and R. Z. Has'minskii“Stochastic approximation and recursive estimation, ” Amer. Math. Soc., vol. 47, Providence, 1973.
11. C. Sunyach, “Une classe de chaines de Markov recurrentes sur un espace metrique complet, ” Ann. Inst. H. Poincare, vol. XI, no. 4, pp. 325–343, 1975.
12. L. Gyorfi, “Stochastic approximation from ergodic sample for linear regression, ” Z. Wahrscheinlickkeitstheorie verw. Geb., vol. 54, pp. 47–55, 1980.
13. J. Fritz, “Learning from an ergodic training sequence. Colloquia Mathematica, ” in Limit Theorems of Probability Theory, P. Revesz Ed. Amsterdam, North-Holland, 1974, pp. 79–91.