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All issues Volume 16 (2012) ESAIM: PS, 16 (2012) 479-526 References
Issue
ESAIM: PS
Volume 16, 2012
Special Issue: Spring School Mons Random differential equations and Gaussian fields
Page(s) 479 - 526
DOI https://doi.org/10.1051/ps/2011108
Published online 08 November 2012
  1. F. Baudoin, An introduction to the geometry of stochastic lows. Imperial Press College, London (2004). [Google Scholar]
  2. J. Bertoin, Sur une intégrale pour les processus à α-variation bornée. Ann. Probab. 17 (1999) 1521–1535. [Google Scholar]
  3. K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula. Ann. Math. 65 (1957) 163–178. [CrossRef] [MathSciNet] [Google Scholar]
  4. K.-T. Chen, Integration of paths; a faithful representation of paths by non-commutative formal power series. Trans. Amer. Math Soc. 89 (1958) 395-407. [MathSciNet] [Google Scholar]
  5. K.-T. Chen, Integration of paths, Bull. Amer. Math. Soc. 83 (1977) 831–879. [Google Scholar]
  6. Z. Ciesielski, G. Kerkyacharian and B. Roynette, Quelques espaces fonctionnels associés à des processus gaussiens. Studia Math. 107 (1993) 171–204. [MathSciNet] [Google Scholar]
  7. L. Coutin and Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields 122 (2002) 108–140. [CrossRef] [MathSciNet] [Google Scholar]
  8. L. Coutin and N. Victoir, Enhanced Gaussian processes and applications. ESAIM Probab. Stat. 13 (2009) 247–260. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  9. A.M. Davie, Differential equations driven by rough paths : an approach via discrete approximation. Appl. Math. Res. Express. AMRX 2 (2007) abm009, 40. [Google Scholar]
  10. A.M. Davie, Uniqueness of solutions of stochastic differential equations. Int. Math. Res. Not. IMRN 24 (2007) rnm124, 26. [Google Scholar]
  11. H. Doss, Liens entre équations différentielles stochastiques et ordinaires. Ann. Inst. Henri Poincaré Sect. B (N.S.) 13 (1977) 99–125. [Google Scholar]
  12. D. Feyel and A. de La Pradelle, Curvilinear integrals along enriched paths. Electron. J. Probab. 11 (2006) 860–892 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  13. P. Friz and N. Victoir, Multidimensional Stochastic Processes as Rough Paths. Theory and Applications. Cambridge University Press (2008). [Google Scholar]
  14. P. Friz and N. Victoir, Differential equations driven by Gaussian signals. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010) 369–413. [Google Scholar]
  15. M. Gubinelli, Controlling rough paths. J. Funct. Anal. 216 (2004) 86–140. [CrossRef] [MathSciNet] [Google Scholar]
  16. Y. Hu and D. Nualart, Rough path analysis via fractional calculus. Trans. Amer. Math. Soc. 361 (2009) 2689–2718. [CrossRef] [MathSciNet] [Google Scholar]
  17. Y. Inahama and H. Kawabi, Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths. J. Funct. Anal. 243 (2007) 270–322. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Lejay, An introduction to rough paths. Séminaire de probabilités, XXXVII 1832 (2003) 1–59. [CrossRef] [Google Scholar]
  19. A. Lejay, Yet another introduction to rough paths. Séminaire de Probabilités, Lect. Notes in Maths XLII (2009) 1–101. [CrossRef] [Google Scholar]
  20. A. Lejay, On rough differential equations. Electron. J. Probab. 14 (2009) 341–364. [CrossRef] [MathSciNet] [Google Scholar]
  21. T. Lyons, Differential equations driven by rough signals. I. An extension of an inequality of L.C. Young. Math. Res. Lett. 1 (1994) 451–464. [CrossRef] [MathSciNet] [Google Scholar]
  22. T.J. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998) 215–310. [CrossRef] [MathSciNet] [Google Scholar]
  23. T. Lyons and Zhongmin Qian, System control and rough paths. Oxford Mathematical Monographs. Oxford University Press, Oxford, Oxford Science Publications (2002). [Google Scholar]
  24. T. Lyons, M. Caruana and T. Lévy, Differential equations driven by rough paths Ecole d’été de probabilités de Saint-Flour XXXIV (2004), Lectures Notes in Math 1908. J. Picard Ed., Springer, Berlin (2007). [Google Scholar]
  25. I. Nourdin, A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one, in Séminaire de probabilités XLI, Lecture Notes in Math. 1934. Springer, Berlin (2008) 181–197. [Google Scholar]
  26. D. Nualart and A. Răşcanu, Differential equations driven by fractional Brownian motion. Collect. Math. 53 (2002) 55–81. [MathSciNet] [Google Scholar]
  27. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives. Gordon and Breach Science Publishers, Yverdon (1993). Theory and applications, Edited and with a foreword by S.M. Nikolski Ed., Translated from the 1987 Russian original, Revised by the authors. [Google Scholar]
  28. E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30. Princeton University Press, Princeton, N.J. (1970). [Google Scholar]
  29. H. Sussmann, On the gap between deterministic and stochastic ordinary differential equations. Ann. Probab. 6 (1978) 19–41. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Tychonoff, Ein Fixpunktsatz. Math. Ann. 111 (1935) 767–776. [CrossRef] [MathSciNet] [Google Scholar]
  31. L.C. Young, An inequality of the Hölder type, connected with Stieltjes integration. Acta Math. 67 (1936) 251–282. [CrossRef] [MathSciNet] [Google Scholar]
  32. M. Zähle, On the link between fractional and stochastic calculus, in Stochastic dynamics, Bremen (1997), Springer, New York (1999) 305–325. [Google Scholar]

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