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References



  1. R.F. Bass, B. Hambly and T.J. Lyons. Extending the Wong-Zakai theorem to reversible Markov processes. J. Eur. Math. Soc., 4(3), 237--269, 2002. DOI:10.1007/s100970200040. Math. Review 1924401

  2. A. Bensoussan, J.L. Lions and G. Papanicolaou. Asymptotic Analysis for Periodic Structures. North-Holland, 1978. Math. Review 0503330

  3. M. Capitaine and C. Donati-Martin. The Lévy area process for the free Brownian motion. J. Funct. Anal., 179(1), 153--169, 2001. DOI:10.1006/jfan.2000.3679. Math. Review 1807256

  4. S. Cohen and A. Estrade. Non-symmetric approximations for manifold-valued semimartingales. Ann. Inst. H. Poincaré Probab. Statist., 36(1), 45--70, 2000. Math. Review 1743093

  5. L. Coutin and Z. Qian. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields, 122(1), 108--140, 2002. DOI:10.1007/s004400100158. Math. Review 1883719

  6. H. Föllmer. Dirichlet processes. In Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980), vol.&npsp;851 of Lecture Notes in Math., pp. 476--478. Springer, Berlin, 1981. Math. Review 0621001

  7. P. Friz. Continuity of the Itô-Map for Hölder rough paths with applications to the support theorem in Hölder norm. ArXiv:math.PR/0304501, Courant Institute (U.S.A.) (preprint), 2003.

  8. P. Friz and N. Victoir. Approximations of the Brownian Rough Path with Applications to Stochastic Analysis. ArXiv:math.PR/0308238, Courant Institute (U.S.A.)/Oxford University (U.-K.) (preprint), 2003.

  9. B. M. Hambly and T. J. Lyons. Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab., 26(1), 132--148, 1998. Math. Review 1617044

  10. N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland, 2nb edition, 1989. Math. Review 1011252

  11. A. Jalubowski, J. Mémin and G. Pagès. Convergence en loi des suites d'intégrales stochastiques sur l'espace D1 de Skorokhod. Probab. Theory Related Fields, 81, pp. 11--137, 1989. Math. Review 0981569

  12. J. Jacod and A.N. Shiryaev. Limit Theorems for Stochastic Processes. Springer-Verlag, 1987. Math. Review 0959133

  13. T.G. Kurtz and P. Protter. Weak Convergence of Stochastic Integrals and Differential Equations. In Probabilistic Models for Nonlinear Partial Differential Equations, Montecatini Terme, 1995, edited by D. Talay and L. Tubaro, vol. 1627 of Lecture Notes in Math., pp. 1--41. Springer-Verlag, 1996. Math. Review 1431298

  14. H. Kunita. Stochastic flows and stochastic differential equations. Cambridge University Press, 1990. Math. Review 1070361

  15. A. Lejay. On the convergence of stochastic integrals driven by processes converging on account of a homogenization property. Electron. J. Probab., 7(18), 1--18, 2002. Math. Review 1943891

  16. A. Lejay. An introduction to rough paths. In Séminaire de Probabilités XXXVII, vol. 1832 of Lecture Notes in Math., 1--59. Springer-Verlag Heidelberg, 2003. Math. Review 2053040

  17. A. Lejay and T.J. Lyons. On the Importance of the Lévy Area for Systems Controlled by Converging Stochastic Processes. Application to Homogenization. In Current Trends in Potential Theory Conference Proceedings, Bucharest, September 2002 and 2003 edited by D. Bakry, L. Beznea, Gh. Bucur, M. Röckner. The Theta Foundation, 2005. MR number not yet available.

  18. M. Ledoux, T. Lyons and Z. Qian. Lévy area of Wiener processes in Banach spaces. Ann. Probab., 30(2), 546--578, 2002. Math. Review 1905851

  19. T. Lyons and Z. Qian. System Control and Rough Paths. Oxford Mathematical Monographs. Oxford University Press, 2002. Math. Review 2036784

  20. M. Ledoux, Z. Qian and T. Zhang. Large deviations and support theorem for diffusions via rough paths. Stochastic Process. Appl., 102(2), 265--283, 2002. DOI:10.1016/S0304-4149(02)00176-X. Math. Review 1935127

  21. T.J. Lyons. Differential equations driven by rough signals. Rev. Mat. Iberoamericana, 14(2), 215--310, 1998. Math. Review 1654527

  22. J. Mémin and L. Slominski. Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques. In Séminaire de Probabilités XXV, vol. 1485 of Lecture Notes in Math., 162--177. Springer-Verlag Heidelberg, 1991. Math. Review 1187779

  23. P. Protter. Approximations of solutions of stochastic differential equations driven by semimartingales. Ann. Probab., 13(3), 716--743, 1985. Math. Review 0799419

  24. P. Protter. Stochastic Integration and Differential Equation, A New Approach. Applications of Mathematics, Springer-Verlag, 1990. Math. Review 1037262

  25. A. Rozkosz and L. Slominski. Extended Convergence of Dirichlet Processes. Stochastics Stochastics Rep., 65(1--2), 79--109, 1998. Math. Review 1708420

  26. D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, 1991. Math. Review 1083357

  27. E.-M. Sipiläinen. A pathwise view of solutions of stochastic differential equations. PhD thesis, University of Edinburgh, 1993.


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