Large deviations for rough paths of the fractional brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 2, pp. 245-271. 
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     title = {Large deviations for rough paths of the fractional brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {245--271},
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Millet, Annie; Sanz-Solé, Marta. Large deviations for rough paths of the fractional brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 2, pp. 245-271. doi : 10.1016/j.anihpb.2005.04.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.04.003/

[1] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2) (2001) 766-801. | MR | Zbl

[2] P. Carmona, L. Coutin, G. Montseny, Stochastic integration with respect to fractional Brownian motion, Ann. Inst. H. Poincaré 39 (1) (2003) 27-68. | Numdam | MR | Zbl

[3] M. Capitaine, C. Donati-Martin, The Lévy area process for the free Brownian motion, J. Funct. Anal. 179 (1) (2001) 153-169. | MR | Zbl

[4] L. Coutin, Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (2002) 108-140. | MR | Zbl

[5] L. Decreusefond, S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1999) 177-214. | MR | Zbl

[6] L. Decreusefond, A Skorohod-Stratonovitch integral for the fractional Brownian motion, in: Stochastic Analysis and Related Topics, VII (Kusadasi, 1998), Progr. Probab., vol. 48, Birkhäuser Boston, Boston, 2001, pp. 177-198. | MR | Zbl

[7] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Appl. Math., vol. 38, Springer-Verlag, 1998. | MR | Zbl

[8] J.-D. Deuschel, D.W. Stroock, Large Deviations, Pure Appl. Math., vol. 137, Academic Press, 1989. | MR | Zbl

[9] P. Fritz, N. Victoir, Approximations of the Brownian rough path with applications to stochastic analysis, prepublication, arXiv, math.PR/0308238, Ann. Inst. H. Poincaré, in press. | Numdam | Zbl

[10] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, 1991. | MR | Zbl

[11] M. Ledoux, T. Lyons, Z. Qian, Lévy area of Wiener processes in Banach spaces, Ann. Probab. 30 (2) (2002) 546-578. | MR | Zbl

[12] M. Ledoux, Z. Qian, T. Zhang, Large deviations and support theorem for diffusion processes via rough paths, Stochastic Proccess. Appl. 102 (2002) 265-283. | MR | Zbl

[13] A. Lejay, An introduction to rough paths, in: Séminaire de Probabilités XXXVII, Lecture Notes in Math., vol. 1832, Springer, Berlin, 2003, pp. 1-59. | MR | Zbl

[14] T.J. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 (1998) 215-310. | MR | Zbl

[15] T. Lyons, Z. Qian, System Control and Rough Paths, Oxford Math. Monographs, Oxford Science Publications, Clarendon Press, Oxford, 2002. | MR | Zbl

[16] B.B. Mandelbrot, J.W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422-437. | MR | Zbl

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