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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 31 open journal systems 


Convergence in Dirichlet Law of Certain Stochastic Integrals

Christophe Chorro, Cermsem, Université Paris 1, France


Abstract
Recently, Nicolas Bouleau has proposed an extension of the Donsker's invariance principle in the framework of Dirichlet forms. He proves that an erroneous random walk of i.i.d random variables converges in Dirichlet law toward the Ornstein-Uhlenbeck error structure on the Wiener space. The aim of this paper is to extend this result to some families of stochastic integrals.


Full text: PDF

Pages: 1005-1025

Published on: July 21, 2005


Bibliography

1. E.  Alòs,  O. Mazet, D.  Nualart, Stochastic calculus with respect to Gaussian processes. In Ann. Probab. 29, no. 2, 766-801, 2001. MR2002g:60083

2. X. Bardina, M. Jolis, Weak convergence to the multiple Stratonovich integral. In Stochastic Process. Appl. 90, no. 2, 277-300, 2000. MR2001k:60074

3. P. Billingsley, Convergence of probability measures. John Wiley & Sons Inc., 1999.

4. N. Bouleau, Théorème de Donsker et formes de Dirichlet. In Bull. Sci. Math. 129, no. 5, 369-380, 2005.

5. N. Bouleau, C. Chorro, Error structures and parameter estimation. In C. R. Acad. Sci. Paris  338, no. 4,  305-310, 2004. MR2005f:62037

6. N. Bouleau, Error calculus for finance and physics: The language of Dirichlet forms, de Gruyter expositions in mathematics 37, 2003. MR2005g:60003

7. N. Bouleau, F. Hirsch, Dirichlet forms and analysis on Wiener space, de Gruyter studies in mathematics 14, 1991. MR93e:60107

8. C. Chorro, On an extension of the central limit theorem to Dirichlet forms, Cahiers de la mse, 2004.80, Univ. Paris 1, 2004.

9. R. Delgado, M. Jolis, Weak approximation for a class of gaussian processes. In J. Appl. Probab.  37, no. 2, 400-407, 2000. MR2001j :60064

10. D. Dacunha-Castelle, M. Duflo, Probabilités et statistiques 2, Masson, 1993.

11. D.Feyel, A. de La Pradelle, Espaces de Sobolev Gaussiens. In Ann. Inst. Fourier 39, no. 4, 875-908, 1989. MR91e:60183

12. M. Fukushima, Dirichlet forms and Markov processes, North-Holland mathematical library 23, 1980. MR81f:60105

13. J. Jacod, A.N. Shiryaev, Limit theorems for stochastic processes, Springer-Verlag, 1987. MR89k:60044

14. A. Jakubowski, J. Mémin, G. Pagès,  Convergence en loi des suites d'intégrales stochastiques sur l'espace D1 de Skorokhod. In Probab. Theory Related  Fields 81, 111-137, 1989. MR90e:60065

15. O. Jonhson, R. Samworth, Central limit theorem and convergence to stable laws in Mallows distance, Preprint, 2004.

16. T.G. Kurtz, P. Protter, Weak limit theorems for stochastic integrals and stochastic differential equations. In Ann. Probab. 19, no. 3, 1035-1070, 1991. MR92k:60130

17. Z. Ma, M. Röckner, Introduction to the theory of (non-symmetric) Dirichlet forms, Springer-Verlag, 1992. MR94d:60119  

18. D. Nualart, Malliavin calculus and related topics, Springer-Verlag, 1995. MR96k:60130

19. D. Nualart, M. Zakai, Multiple Wiener-Itô integrals possessing a continuous extension, Probab. Theory Related Fields 85, no. 1, 131-145, 1990. MR92e:60109

20. A.W. Van der Vaart, J.A. Wellner, Weak convergence and empirical processes, Springer-Verlag,  1996.

 

















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Electronic Journal of Probability. ISSN: 1083-6489