Sur quelques algorithmes récursifs pour les probabilités numériques

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1. [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. Zbl0790.60047MR1354161
2. [2] D.G. Aronson, Bounds for the fundamental solution of a parabolic equation. Bull. Amer. Math. Soc. 73 (1967) 890-903. Zbl0153.42002MR217444
3. [3] J.G. Attali, Méthodes de stabilité pour les chaînes de Markov non fellériennes, Thèse de l’Université Paris I (1999). 
4. [4] G. Basak et R. Bhattacharya, Stability in distributions for a class of singular diffusions. Ann. Probab. 20 (1992) 312-321. Zbl0749.60073MR1143422
5. [5] G.K. Basak, I. Hu et C.-Z. Wei, Weak convergence of recursions. Stochastic Process. Appl. 68 (1997) 65-82. Zbl0923.60026MR1454579
6. [6] M. Benaïm, Recursive Algorithms, Urn process and Chaining Number of Chain Recurrent sets. Ergodic Theory Dynam. Systems 18 (1997) 53-87. Zbl0921.60061MR1609499
7. [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. Zbl0955.62085MR1767993
8. [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. Zbl0734.60027MR1133372
9. [9] A. Benveniste, M. Métivier et P. Priouret, Algorithmes adaptatifs et approximations stochastiques. Masson, Paris (1987) 367p. Zbl0639.93002
10. [10] S. Borovkov, Ergodicity and Stability of Stochastic Processes. Wiley Chichester (England), Wiley Ser. Probab. Stat. (1998) 585p. Zbl0917.60005MR1658404
11. [11] C. Bouton, Approximation gaussienne d’algorithmes à dynamique markovienne. Ann. Inst. H. Poincaré B 24 (1988) 131-155. Zbl0643.60038
12. [12] O. Brandière et M. Duflo, Les algorithmes stochastiques contournent-ils les pièges ? Ann. Inst. H. Poincaré 32 (1996) 395-477. Zbl0849.62043MR1387397
13. [13] G.A. Brosamler, An almost everywhere central limit theorem. Math. Proc. Cambridge Philos. Soc. 104 (1988) 561-574. Zbl0668.60029MR957261
14. [14] I. Berkes, E. Csáki, A universal result in almost sure central limit theory. Stochastic Process. Appl. 94 (2001) 105-134. Zbl1053.60022MR1835848
15. [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). 
16. [16] S. Cheng et L. Peng, Almost sure convergence in extreme value theory. Math. Nachr. 190 (1998) 43-50. Zbl0932.60028MR1611675
17. [17] M. Duflo, Random Iterative systems. Springer, Berlin (1998). 
18. [18] N. Dunford et J.T. Schwartz, Linear Operators. Wiley-Interscience, New-York (1958). Zbl0084.10402
19. [19] S. Ethier et T. Kurtz, Markov Processes, characterization and convergence. Wiley, New-York, Wiley Ser. Probab. Math. Statist. (1986) 534p. Zbl0592.60049MR838085
20. [20] J.C. Fort et G. Pagès, Asymptotic behaviour of a Markov constant step stochastic algorithm. SIAM J. Control Optim. 37 (1999) 1456-1482. Zbl0954.60057MR1710228
21. [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). 
22. [22] A. Fisher, Convex invariant means and a pathwise central limit theorem. Adv. Math. 63 (1987) 213-246. Zbl0627.60034MR877784
23. [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. Zbl0962.60073MR1671843
24. [24] P. Hall et C.C. Heyde, Martingale Limit Theory and its Application. Academic Press, New-York (1980) 308p. Zbl0462.60045MR624435
25. [25] R.Z. Has’minskii, Stochastic stability of differential equations. Sijthoff & Noordhoff, Alphen aan den Rijn (The Nederlands) (1980) 344p. 
26. [26] I. Karatzas et S. Shreve, Brownian Motion and Stochastic Calculus. Springer-Verlag, New-York (1988) (2nd Ed., 1992) 470p. Zbl0638.60065MR917065
27. [27] S. Karlin et H. Taylor, A second course in stochastic processes. Academic Press, New-York (1981) 542p. Zbl0469.60001MR611513
28. [28] Y. Kifer, Random perturbations of Dynamical Systems. Birkhaäuser, Progr. Probab. Statist. (1988) 294p. Zbl0659.58003MR1015933
29. [29] U. Krengel, Ergodic Theorems. de Gruyter Stud. Math. (1989) 357p. Zbl0575.28009MR797411
30. [30] H.J. Kushner et D.S. Clark, Stochastic Approximation for Constrained and Unconstrained Systems. Springer, Appl. Math. Sci. 26 (1978) 261p. Zbl0381.60004MR499560
31. [31] H.J. Kushner, Approximation and weak convergence methods for random processes and applications to stochastic system theory. MIT Cambridge (1985). Zbl0551.60056MR741469
32. [32] H.J. Kushner et H. Huang, Rates of convergence for stochastic approximation type algorithms. SIAM J. Control Optim. 17 (1979) 607-617. Zbl0418.93093MR540841
33. [33] D. Lamberton et G. Pagès, Recursive computation of the invariant measure of a diffusion. Bernoulli (à paraître). Zbl1006.60074
34. [34] M.T. Lacey et W. Philip, A note on the almost sure central limit theorem. Statist. Probab. Lett. 9 (1990) 201-205. Zbl0691.60016MR1045184
35. [35] S. Meyn et R. Tweedie, Markov chains and Stochastic Stability. Springer (1993) 550p. Zbl0925.60001MR1287609
36. [36] M. Pelletier, Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing. Ann. Appl. Probab. 8 (1998) 10-44. Zbl0965.62065MR1620405
37. [37] M. Pelletier, An almost sure central limit theorem for stochastic algorithms. J. Multivariate Anal. 71 (1999) 76-93. Zbl0951.62071MR1721961
38. [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). Zbl0865.60020MR1416182
39. [39] B.T. Polyak, New Stochastic Approximation type procedures. Avtomat. i Telemakh. 7 (1990), in Russian, Automat. Remote Control 51 (1990) 107-118. MR1071220
40. [40] D. Revuz et M. Yor, Continuous martingales and Brownian Motion, 2nd Ed. Springer, Berlin (1991) 557p. Zbl0731.60002MR1083357
41. [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). 
42. [42] P. Schatte, On strong versions of the central limit theorem. Math. Nachr. 137 (1988) 249-256. Zbl0661.60031MR968997
43. [43] D.W. Stroock, Probability Theory : An analytic view. Cambridge University Press (revised edition, 1994) 512p. Zbl0925.60004MR1267569
44. [44] D. Talay, Second order discretization of stochastic differential systems for the computation of the invariant law. Stochastics Stochastics Rep. 29 (1990) 13-36. Zbl0697.60066
45. [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. Zbl0718.60058MR1091544
46. [46] A. Touati, Sur les versions fortes du théorème de la limite centrale. Pré-pub. de l’Université de Marne-la-Vallée (1995). 

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