Free Access
Volume 17, 2013
Page(s) 179 - 194
Published online 08 February 2013
  1. A. Benveniste, M. Métivier and P. Priouret, Adaptive Algorithms and Stochastic Approximations. Springer-Verlag, New York, Appl. Math. 22 (1990). [Google Scholar]
  2. B. Bercu, On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications. Stoc. Proc. Appl. 111 (2004) 157–173. [Google Scholar]
  3. B. Bercu and J.-C. Fort, A moment approach for the almost sure central limit theorem for martingales. Stud. Sci. Math. Hung. (2006). [Google Scholar]
  4. B. Bercu, P. Cènac and G. Fayolle, On the almost sure central limit theorem for vector martingales : Convergence of moments and statistical applications. J. Appl. Probab. 46 (2009) 151–169. [CrossRef] [Google Scholar]
  5. G.A. Brosamler, An almost everywhere central limit theorem. Math. Proc. Cambridge Philos. Soc. 104 (1988) 213–246. [Google Scholar]
  6. F. Chaâbane, Version forte du théorème de la limite centrale fonctionnel pour les martingales. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996) 195–198. [MathSciNet] [Google Scholar]
  7. F. Chaâbane, Invariance principles with logarithmic averaging for martingales. Stud. Sci. Math. Hung. 37 (2001) 21–52. [Google Scholar]
  8. F. Chaâbane and F. Maâouia, Théorèmes limites avec poids pour les martingales vectorielles. ESAIM : PS 4 (2000) 137–189 (electronic). [CrossRef] [EDP Sciences] [Google Scholar]
  9. F. Chaâbane, F. Maâouia and A. Touati, Génèralisation du théorème de la limite centrale presque-sûr pour les martingales vectorielles. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 229–232. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Duflo, Random Iterative Methods. Springer-Verlag (1997). [Google Scholar]
  11. P. Dupuis and H.J. Kushner, Stochastic approximation and large deviations : Upper bounds and w.p.l convergence. SIAM J. Control Optim. 27 (1989) 1108–1135. [CrossRef] [MathSciNet] [Google Scholar]
  12. W. Feller, An introduction to probability theory and its applications II. John Wiley, New York (1966). [Google Scholar]
  13. P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application. Academic Press, New York, NY (1980). [Google Scholar]
  14. V. Koval and R. Schwabe, Exact bounds for the rate of convergence of stochastic approximation procédures. Stoc. Anal. Appl. 16 (1998) 501–515. [CrossRef] [Google Scholar]
  15. H.J. Kushner and D.S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer-Verlag, Berlin (1978). [Google Scholar]
  16. M. Lacey and W. Phillip, A note on the almost sure central limit theorem. Stat. Probab. Lett. 9 (1990) 201–205. [CrossRef] [MathSciNet] [Google Scholar]
  17. D. Lamberton and G. Pagès, Recursive computation of the invariant distribution of a diffusion. Bernoulli 8 (2002) 367–405. [MathSciNet] [Google Scholar]
  18. D. Lamberton and G. Pagès, Recursive computation of the invariant distribution of a diffusion : the case of a weakly mean reverting drift. Stoch. Dyn. 3 (2003) 435–451. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Le Breton, About the averaging approach schemes for stochastic approximations. Math. Methods Stat. 2 (1993) 295–315. [Google Scholar]
  20. A. Le Breton and A. Novikov, Averaging for estimating covariances in stochastic approximation. Math. Methods Stat. 3 (1994) 244–266. [Google Scholar]
  21. A. Le Breton and A. Novikov, Some results about averaging in stochastic approximation. Metrika 42 (1995) 153–171. [CrossRef] [Google Scholar]
  22. M.A. Lifshits, Lecture notes on almost sure limit theorems. Publications IRMA 54 (2001) 1–25. [Google Scholar]
  23. M.A. Lifshits, Almost sure limit theorem for martingales, in Limit theorems in probability and statistics II (Balatonlelle, 1999). János Bolyai Math. Soc., Budapest (2002) 367–390. [Google Scholar]
  24. L. Ljung, G. Pflug and H. Walk, Stochastic Approximation and Optimization of Random Systems. Birkhäuser, Boston (1992). [Google Scholar]
  25. A. Mokkadem and M. Pelletier, A companion for the Kiefer–Wolfowitz–Blum stochastic approximation algorithm. Ann. Stat. (2007). [Google Scholar]
  26. M. Pelletier, On the almost sure asymptotic behaviour of stochastic algorithms. Stoch. Proc. Appl. 78 (1998) 217–244. [Google Scholar]
  27. M. Pelletier, An almost sure central limit theorem for stochastic approximation algorithms. J. Multivar. Anal. 71 (1999) 76–93. [CrossRef] [MathSciNet] [Google Scholar]
  28. H. Robbins and S. Monro, A stochastic approximation method. Ann. Math. Stat. 22 (1951) 400–407. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Schatte, On strong versions of central limit theorem. Math. Nachr. 137 (1988) 249–256. [CrossRef] [MathSciNet] [Google Scholar]
  30. Y. Zhu, Asymptotic normality for a vector stochastic difference equation with applications in stochastic approximation. J. Multivar. Anal. 57 (1996) 101–118. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.