A note on the notion of geometric rough paths

Probability Theory and Related Fields

Volumn 136, Issue 3, 2006, Pages 395-416

  Friz, Peter ^a   Victoir, Nicolas ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747890718     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0487-7     Document Type: Article

References (27)

1. a and m. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8, 217-222 (1960)
2. Coutin, L., Qian Z.: Stochastic analysis, rough path analysis and fractional Brownian motions Probab. Theory Relat. Fields 122, 108-140 (2002)
3. Decreusefond, L., Üstünel, A.S.: Stochastic Analysis of the Fractional Brownian Motion, Potential Analysis 10, 177-214 (1997)
4. Dudley, R.M., Norvaisa, R.: An introduction to p-variation and Young integrals. Lecture notes.
5. Folland, G.B., Stein, E.M.: Hardy spaces on homogeneous groups. Mathematical Notes, 28. Princeton University Press, 1982
6. De La Pradelle, A., Feyel, D.: Curvilinear Integrals along Rough Paths. Preprint
7. Friz, P.: Continuity of the Ito-map for Hoelder rough paths with applications to the support theorem in Hölder norm, Probability and PDEs in Modern Applied Mathematics, The IMA Volumes in Mathematics and its Applications, Vol. 140, 2005
8. Friz, P., Lyons, T., Stroock, D.: Lévy's area under conditioning, Annales de l'Institut Henri Poincare (B), Probability and Statistics, 2005. To appear
9. Friz, P., Victoir, N.: Approximations of the Brownian Rough Path with Applications to Stochastic Analysis, Annales de l'Institut Henri Poincare (B), Probability and Statistics, Volume 41, Issue 4, 2005, pp. 703-724
10. Goodman, R.: Filtrations and Asymptotic Automorphisms on Nilpotent Lie Groups. J. Diff. Geometry 12, 183-196 (1977)
11. Haynes, G.W., Hermes H.: Nonlinear Controllability via Lie Theory. SIAM J. Control Optim. 8 (4), 450-460 (1970)
12. Kurzweil, J., Jarnik, J.: Limit Process in Ordinary Differential Equations". J. Appl. Math. Phys. 38, 241-256 (1987)
13. Kurzweil, J., Jarnik, J.: Iterated Lie Brackets in Limit Processes in Ordinary Differential Equations. Results in Mathematics 14, 125-137 (1988)
14. Kurzweil, J., Jarnik, J.: A Convergence Effect in Ordinary Differential Equations. Asym. Meth. Math. Physics (Russian), 301, 'Naukova Pumka', Kiev, 1989
15. Lejay, A.: Introduction to Rough Paths, Séminaire de Probabilité, Springer. To appear
16. Ledoux, M., Qian, Z., Zhang, T.: Large deviations and support theorem for diffusion processes via rough paths. Stochastic Process. Appl. 102 (2), 265-283 (2002)
17. Liu, W.: An approximation algorithm for nonholonomic systems. SIAM J. Control Optim. 35 (4), 1328-1365 (1997)
18. Liu, W.S.: Averaging Theorems for Highly Oscillatory Differential Equations and Iterated Lie Brackets." SIAM J. Control Optim. 35 (6), (1997)
19. Liu, W., Sussman, H.: Shortest paths for sub-Riemannian metrics on rank-two distributions. Mem. Amer. Math. Soc. 118 (564), (1995)
20. Lyons, T.: Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (2), 215-310 (1998)
21. Lyons, T., Qian, Z.: System Control and Rough Paths, Oxford University Press, 2002
22. Lyons, T., Victoir, N.: An Extension Theorem to Rough Path. Preprint
23. Malliavin, P.: Stochastic Analysis, Springer, 1997
24. Montgomery, R.: A tour of subriemannian geometries, their geodesies and applications. Math.Surveys and Monographs 91. AMS, 2002
25. Musielak, J., Semadeni, Z.: Some classes of Banach spaces depending on a parameter. Studia Math. 20, 271-284 (1961)
26. Sussmann, HJ., Liu, W.: Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories." IEEE Publications, New York, 1991, pp. 431-442
27. Wiener, N.: The quadratic variation of a function and its Fourier coefficients. J. Math, and Phys. 3, 72-94 (1924)