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. [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. [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. [Google Scholar]
  14. I. Berkes, E. Csáki, A universal result in almost sure central limit theory. Stochastic Process. Appl. 94 (2001) 105-134. [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. [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. [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]

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.