Some Notes on Large Deviations of Markov Processes

Acta Mathematica Sinica, English Series

Volumn 16, Issue 3, 2000, Pages 369-394

  Wu, Liming ^a,b  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b WUHAN UNIVERSITY   (China)

Author keywords

Hyper exponential recurrence; Large deviations; Uniformly integrable operators; topology

Indexed keywords

EID: 0346679040     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011549     Document Type: Article

References (31)

1. M D Donsker, S R S Varadhan. Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm Pur Appl Math, 1975, 28: 1-47, 279-301; 1976, 29: 389-461; 1983, 36: 183-212
2. M D Donsker, S R S Varadhan. Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm Pur Appl Math, 1975, 28: 1-47, 279-301; 1976, 29: 389-461; 1983, 36: 183-212
3. M D Donsker, S R S Varadhan. Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm Pur Appl Math, 1975, 28: 1-47, 279-301; 1976, 29: 389-461; 1983, 36: 183-212
4. J D Deuschel, D W Stroock. Large Deviations. Pure and Appl Math 137, Academic Press 1989
5. A Dembo, O Zeitonni. Large Deviations Techniques and Applications. Second Edition, Springer 1998
6. L M Wu. Grandes deviations pour les processus de Markov essentiellement irréductibles. I: temps discret, C RAS, Série I, 1991, 312: 608-614; II: temps continu, C R A S, Série I, 1992, 314: 941-946; III: applications, C R A S, Série I, 1993, 316: 853-858 (the complete version is contained in my Habilitation à diriger des recherches. Laboratoire de Probabilités. Université Paris VI, 1993)
7. L M Wu. Grandes deviations pour les processus de Markov essentiellement irréductibles. I: temps discret, C RAS, Série I, 1991, 312: 608-614; II: temps continu, C R A S, Série I, 1992, 314: 941-946; III: applications, C R A S, Série I, 1993, 316: 853-858 (the complete version is contained in my Habilitation à diriger des recherches. Laboratoire de Probabilités. Université Paris VI, 1993)
8. L M Wu. Grandes deviations pour les processus de Markov essentiellement irréductibles. I: temps discret, C RAS, Série I, 1991, 312: 608-614; II: temps continu, C R A S, Série I, 1992, 314: 941-946; III: applications, C R A S, Série I, 1993, 316: 853-858 (the complete version is contained in my Habilitation à diriger des recherches. Laboratoire de Probabilités. Université Paris VI, 1993)
9. L M Wu. Uniformly integrable operators and large deviations for Markov processes. Journ Funct Anal 2000, 172: 301-376
10. A de Acosta. Large deviations for vector valued additive functionals of a Markov process: lower bound. Ann Probab, 1988, 16: 925-960
11. N C Jain. Large deviations for additive functionals of Markov processes. Ann Probab, 1990, 17(3): 1073-1098
12. J Gärtner. On large deviations from the invariant measures. Theory Probab. Appl, 1977, 7: 239-246
13. R S Ellis. Large Deviations and Statistical Mechanics, Springer, Berlin 1985
14. D W Stroock. An Introduction to The Theory of Large Deviations. Springer Berlin 1984
15. D W Dawson, J Gärtner. Long time fluctuation of weakly interacting diffusions. Stochastic, 1987, 20: 247-308
16. C Léonard. Large deviations in the dual of a normed space. Preprint 1992
17. L M Wu. Some general methods of large deviations and applications, in Habilitation à diriger des recherches, Laboratoire de Probabilites, Université Paris VI, 1993
18. E Bolthausen. Markov processes large deviations in the τ-topology. Stochastic Processes and Appl, 1987, 151: 161-177
19. A de Acosta. Large deviations for empirical measures of Markov chains. Journ Theo Probab, 1990, 3: 395-431
20. J Baxter, N Jain, S R S Varadhan. Some familiar examples for which the large deviation principle does not hold. Comm on Pure & Applied Mathematics, 1991, 34: 911-923
21. W Bryc, W Smolenski. On the convergence of averages of mixing sequences. Journ Theo Proba, 1993, 6(3): 473-483
22. E B Davies, B Simon. Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians. J Funct Anal, 1984, 59: 335-395
23. E Nummelin. General Irreducible Markov Chains and Non-Negative Operators. Cambridge Tracts in Math 83. Cambridge University Press, 1984
24. K L Chung. Markov Chains with Stationary Transition Probability. Second Edition, Springer Verlag, 1967
25. S R S Varadhan. Large Deviations and Applications. Ecole d'Eté de Probabilités de Saint-Flour XV-XVII, 1985. Editor: P L Hennequin, Lect Notes in Math 1362: 3-49, Springer 1988.
26. N Ikeda, S Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland/Kodansha, 1981
27. R Z Has'minski. Stochastic Stability of Differential Equations. Translated by D Louvish, Sijthoff & Noordhoff, 1980
28. Z M Ma, M Röckner. An Introduction to the Theory of (Non-Symmetric) of Dirichlet Forms. Springer-Verlag, 1992
29. D Revuz, M Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, 1991
30. L M Wu. Feynman-Kac semigroups, ground state diffusions and large deviations. Journ Funct Anal, 1994, 123(1): 202-231
31. A Friedman. Partial Differential Equations. Holt, Rinehart & Winston, 1969