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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 8 open journal systems 


The Principle of Large Deviations for Martingale Additive Functionals of Recurrent Markov Processes

Matthias K. Heck, HypoVereinsbank
Faïza Maaouia, HypoVereinsbank


Abstract
We give a principle of large deviations for a generalized version of the strong central limit theorem. This generalized version deals with martingale additive functionals of a recurrent Markov process.


Full text: PDF

Pages: 1-26

Published on: March 2, 2001
Bibliography
  1. G. A. BROSAMLER (1988). An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. , 104, 561-574 Math. Review 89i:60045
  2. G. A. BROSAMLER (1990). A simultaneous almost everywhere central limit theorem, for diffusions and its application to path energy and eigenvalues of the Laplacian, Illinois J. Math., 34 526-556 Math. Review 91i:60189
  3. I.BERKES and H. DEHLING (1993). Some limit theorems in log density, Ann. Probab. Vol. 23, No. 3, 1640-1670 Math. Review 94h:60026
  4. F. CHAABANE F. MAAOUIA and A. TOUATI (1998). Généralisation du théorème de la limite centrale presque-sûre pour les martingales vectorielles, C. R. Acad. Sci. Paris, T 326, Série I, 229-232. Math. Review 99i:60061
  5. F. CHAABANE (2001). Invariance principles with logarithmic averaging for martingales, To appear in Studia Math. Sci. Hungar. Math. Review number not available.
  6. M. CSÖRGÖ, L. HORVÁTH (1992). Invariance principles for logarithmic averages, Proc. Camb. Phil. Soc., 112-195. Math. Review 93e:60057
  7. D. DACUNHA-CASTELLE and M. DUFLO (1983). Probabililés et statistiques (2. Problèmes à temps mobiles), Masson, (1983). Math. Review 85k:60001
  8. J. D. DEUSCHEL and D. W. STROOCK (1989). Large deviations, Academic Press. Math. Review 90h:60026
  9. M. D. DONSKER (1951). An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. 6, Math. Review 12,723a
  10. M. DUFLO (1997). Random iterative models, Masson Math. Review 98m:62239
  11. D. FREEDMAN (1983). Brownian motion and diffusion, Springer, New York, Second edition Math. Review 84c:60121
  12. P. HALL and C. C. HEYDE (1980). Martingale limit theory and its application. Probability and Mathematical Statistics, Academic Press Math. Review 83a:60001
  13. M. K. HECK (1995). Das Prinzip der gzo(beta )en Abweichungen fur fas sicheren Zentralen Grenzwertsatz und fur seine funktionale Verallgemeinerung, Dissertation, Saarbrucken, Germany Math. Review number not avilable
  14. M. K. HECK (1998). The principle of large deviations for the almost everywhere central limit theorem. Stoch, Process Appl. 76, No 1, 61-75. Math. Review 99f:60059
  15. M. K. HECK (1999). Principle of large deviations for the empirical processes of Ornstein-Uhlenbeck Process, J. Theoret. Probab. 12, No 1, 147-179. Math. Review 2000f:60042
  16. J. T. HULL (1997). Options, futures, and other deviatives Prentice-Hall, Upper Saddle River, Math. Review number not available
  17. M. T. LACEY and W. PHILLIP (1990). A note on the almost sure central limit theorem, Statist. Probab. Let. 9, 201-205. Math. Review 91e:60100
  18. M. A. LIFSHITS and E. S. STANKEVICH (2001). On the Large Deviation Principle for the Almost Sure CLT, Preprint Université de Lille, France. Math. Review number not available
  19. F. MAAOUIA (1987). Comportements asymptotiques des fonctionnelles additives des processus de Markov récurrents au sens de Harris, Thèse de 3ème cycle, Université de Paris VII. Math. Review number not available
  20. F. MAAOUIA (1996). Versions fortes du théorème de la limite centrale pour les processus de Markov, C. R. Acad. Sci. Paris, T 323, Série I, 293-296. Math. Review 97c:60182
  21. F. MAAOUIA (2001). Principes d'invariance par moyennisation logarithmique pour les processus de Markov, To appear in The Annals of Probability. Math. Review number not available
  22. P. MARCH and T. SEPPALAINEN (1997). Large deviations from the almost everywhere central limit theorem, J. Theor. Probab. 10, 935-965. Math. Review 98m:60040
  23. S. P. MEYN and R. L. TWEEDIE (1993). Markov Chains and Stochastic Stability, Springer. Math. Review 98m:60040
  24. E. NUMMELIN (1983). General irreducible Markov chains and negative operators, Cambridge University Press. Math. Review 90k:60131
  25. E. NUMMELIN and R. L. TWEEDIE (1978). Geometric ergodicity and R-positivity for general Markov chains, Ann. of Probab. Vol. 6, 404-420. Math. Review 57 #7773
  26. B. RODZIK and Z. RYCHLIK (1994). An almost sure central limit theorem for independent random variables, Ann. IHP Vol. 30, No. 1, 1-11. Math. Review 95c:60029
  27. P. SCHATTE (1988). On strong versions of the central limit theorem, Math. Nachr. 137, 249-256. Math. Review 89g:60114
  28. A. TOUATI (1990). Loi fonctionnelle du logarithme itéré pour des processus de Markov récurrents, Ann. Prob. Vol. 18, No. 1, 140-159. Math. Review 92a:60094
  29. A. TOUATI (1995). Sur les versions fortes du théoerème de la limite centrale, Preprint Université de Marne-La-Vallée, No 23. Math. Review numbernot available
  30. S. R. S. VARADHAN (1984). Large deviations and applications, SIAM, Philadelphia, (1984). Math. Review 86h:60067b
















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Electronic Journal of Probability. ISSN: 1083-6489