Free Access
Issue
ESAIM: PS
Volume 5, 2001
Page(s) 141 - 170
DOI https://doi.org/10.1051/ps:2001106
Published online 15 August 2002
  1. S. Aida , S. Kusuoka et D.W. Stroock, On the support of Wiener functionals, dans Asymptotic problems in Probability Theory: Wiener Functionals and Asymptotics, édité par K.D. El Worthy et N. Ikeda. Longman Scient. and Tech., New-York, Pitman Res. Notes Math. Ser. 284 (1993) 3-34. [Google Scholar]
  2. D.G. Aronson, Bounds for the fundamental solution of a parabolic equation. Bull. Amer. Math. Soc. 73 (1967) 890-903. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.G. Attali, Méthodes de stabilité pour les chaînes de Markov non fellériennes, Thèse de l'Université Paris I (1999). [Google Scholar]
  4. G. Basak et R. Bhattacharya, Stability in distributions for a class of singular diffusions. Ann. Probab. 20 (1992) 312-321. [CrossRef] [MathSciNet] [Google Scholar]
  5. G.K. Basak, I. Hu et C.-Z. Wei, Weak convergence of recursions. Stochastic Process. Appl. 68 (1997) 65-82. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Benaïm, Recursive Algorithms, Urn process and Chaining Number of Chain Recurrent sets. Ergodic Theory Dynam. Systems 18 (1997) 53-87. [Google Scholar]
  7. M. Benaïm, Dynamics of Stochastic Approximation Algorithms, Séminaire de Probabilités XXXIII, édité par J. Azéma, M. Émery, M. Ledoux et M. Yor. Springer, Lecture Notes in Math. 1709 (1999) 1-68. [Google Scholar]
  8. G. Ben Arous et R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale (II). Probab. Theory Related Fields 90 (1991) 377-402. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Benveniste, M. Métivier et P. Priouret, Algorithmes adaptatifs et approximations stochastiques. Masson, Paris (1987) 367p. [Google Scholar]
  10. S. Borovkov, Ergodicity and Stability of Stochastic Processes. Wiley Chichester (England), Wiley Ser. Probab. Stat. (1998) 585p. [Google Scholar]
  11. C. Bouton, Approximation gaussienne d'algorithmes à dynamique markovienne. Ann. Inst. H. Poincaré B 24 (1988) 131-155. [Google Scholar]
  12. O. Brandière et M. Duflo, Les algorithmes stochastiques contournent-ils les pièges ? Ann. Inst. H. Poincaré 32 (1996) 395-477. [Google Scholar]
  13. G.A. Brosamler, An almost everywhere central limit theorem. Math. Proc. Cambridge Philos. Soc. 104 (1988) 561-574. [CrossRef] [MathSciNet] [Google Scholar]
  14. I. Berkes, E. Csáki, A universal result in almost sure central limit theory. Stochastic Process. Appl. 94 (2001) 105-134. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Chaâbane, F. Maâouia et A. Touati, Versions fortes associées aux théorèmes limites en loi pour les martingales vectorielles. Pré-pub. de l'Université de Bizerte, Tunisie (1996). [Google Scholar]
  16. S. Cheng et L. Peng, Almost sure convergence in extreme value theory. Math. Nachr. 190 (1998) 43-50. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Duflo, Random Iterative systems. Springer, Berlin (1998). [Google Scholar]
  18. N. Dunford et J.T. Schwartz, Linear Operators. Wiley-Interscience, New-York (1958). [Google Scholar]
  19. S. Ethier et T. Kurtz, Markov Processes, characterization and convergence. Wiley, New-York, Wiley Ser. Probab. Math. Statist. (1986) 534p. [Google Scholar]
  20. J.C. Fort et G. Pagès, Asymptotic behaviour of a Markov constant step stochastic algorithm. SIAM J. Control Optim. 37 (1999) 1456-1482. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.C. Fort et G. Pagès, Stochastic algorithms with non constant step: a.s. behaviour of weighted empirical measures. Pré-pub. Université Paris 12 Val-de-Marne (1998, soumis). [Google Scholar]
  22. A. Fisher, Convex invariant means and a pathwise central limit theorem. Adv. Math. 63 (1987) 213-246. [CrossRef] [Google Scholar]
  23. H. Ganidis, B. Roynette et F. Simonot, Convergence rate of some semi-groups to their invariant probability. Stochastic Process. Appl. 79 (1999) 243-264. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Hall et C.C. Heyde, Martingale Limit Theory and its Application. Academic Press, New-York (1980) 308p. [Google Scholar]
  25. R.Z. Has'minskii, Stochastic stability of differential equations. Sijthoff & Noordhoff, Alphen aan den Rijn (The Nederlands) (1980) 344p. [Google Scholar]
  26. I. Karatzas et S. Shreve, Brownian Motion and Stochastic Calculus. Springer-Verlag, New-York (1988) (2nd Ed., 1992) 470p. [Google Scholar]
  27. S. Karlin et H. Taylor, A second course in stochastic processes. Academic Press, New-York (1981) 542p. [Google Scholar]
  28. Y. Kifer, Random perturbations of Dynamical Systems. Birkhaäuser, Progr. Probab. Statist. (1988) 294p. [Google Scholar]
  29. U. Krengel, Ergodic Theorems. de Gruyter Stud. Math. (1989) 357p. [Google Scholar]
  30. H.J. Kushner et D.S. Clark, Stochastic Approximation for Constrained and Unconstrained Systems. Springer, Appl. Math. Sci. 26 (1978) 261p. [Google Scholar]
  31. H.J. Kushner, Approximation and weak convergence methods for random processes and applications to stochastic system theory. MIT Cambridge (1985). [Google Scholar]
  32. H.J. Kushner et H. Huang, Rates of convergence for stochastic approximation type algorithms. SIAM J. Control Optim. 17 (1979) 607-617. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Lamberton et G. Pagès, Recursive computation of the invariant measure of a diffusion. Bernoulli (à paraître). [Google Scholar]
  34. M.T. Lacey et W. Philip, A note on the almost sure central limit theorem. Statist. Probab. Lett. 9 (1990) 201-205. [CrossRef] [MathSciNet] [Google Scholar]
  35. S. Meyn et R. Tweedie, Markov chains and Stochastic Stability. Springer (1993) 550p. [Google Scholar]
  36. M. Pelletier, Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing. Ann. Appl. Probab. 8 (1998) 10-44. [CrossRef] [MathSciNet] [Google Scholar]
  37. M. Pelletier, An almost sure central limit theorem for stochastic algorithms. J. Multivariate Anal. 71 (1999) 76-93. [CrossRef] [MathSciNet] [Google Scholar]
  38. M. Pelletier, Efficacité asymptotique presque sûre des algorithmes stochastiques moyennisés. C. R. Acad. Sci. Paris Série I 323 (1996) 813-816 ; développé dans Asymptotic almost sure efficiency of averaged stochastic algorithms (soumis). [Google Scholar]
  39. B.T. Polyak, New Stochastic Approximation type procedures. Avtomat. i Telemakh. 7 (1990), in Russian, Automat. Remote Control 51 (1990) 107-118. [Google Scholar]
  40. D. Revuz et M. Yor, Continuous martingales and Brownian Motion, 2nd Ed. Springer, Berlin (1991) 557p. [Google Scholar]
  41. D. Ruppert, Efficient estimators from a slowly convergent Robbins-Monro Process, Technical Report, School of Operations Research and Industrial, Engineering. Cornell University, Ithaca, NY, No. 781 (1985). [Google Scholar]
  42. P. Schatte, On strong versions of the central limit theorem. Math. Nachr. 137 (1988) 249-256. [CrossRef] [MathSciNet] [Google Scholar]
  43. D.W. Stroock, Probability Theory: An analytic view. Cambridge University Press (revised edition, 1994) 512p. [Google Scholar]
  44. D. Talay, Second order discretization of stochastic differential systems for the computation of the invariant law. Stochastics Stochastics Rep. 29 (1990) 13-36. [Google Scholar]
  45. D. Talay et L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 (1990) 94-120. [Google Scholar]
  46. A. Touati, Sur les versions fortes du théorème de la limite centrale. Pré-pub. de l'Université de Marne-la-Vallée (1995). [Google Scholar]

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