Free Access
Issue
ESAIM: PS
Volume 10, September 2006
Page(s) 356 - 379
DOI https://doi.org/10.1051/ps:2006015
Published online 08 September 2006
  1. D.G. Aronson, Non-negative solutions of linear parabolic equation. Ann. Scuola Norm. Sup. Pisa 22 (1968) 607–693. [MathSciNet] [Google Scholar]
  2. R.F. Bass, B. Hambly and T.J. Lyons, Extending the Wong-Zakai theorem to reversible Markov processes. J. Eur. Math. Soc. 4 (2002) 237–269. [CrossRef] [MathSciNet] [Google Scholar]
  3. K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula. Ann. of Math. 65 (1957) 163–178. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Coutin and A. Lejay, Semi-martingales and rough paths theory. Electron. J. Probab. 10 (2005) 761–785. [MathSciNet] [Google Scholar]
  5. 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]
  6. F. Coquet and L. Słomiński, On the convergence of Dirichlet processes. Bernoulli 5 (1999) 615–639. [CrossRef] [MathSciNet] [Google Scholar]
  7. K. Dupoiron, P. Mathieu and J. San martin, Formule d'Itô pour des diffusions uniformément elliptiques et processus de Dirichlet. Potential Anal. 21 (2004) 7–3. [CrossRef] [MathSciNet] [Google Scholar]
  8. H. Föllmer, Calcul d'Itô sans probabilités, in Séminaire de Probabilités, XV. Lect. Notes Math. 850 (1981) 143–150. Springer, Berlin. [CrossRef] [Google Scholar]
  9. H. Föllmer, Dirichlet processes, in Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980). Lect. Notes Math. 851 (1981) 476–478. Springer, Berlin. [CrossRef] [Google Scholar]
  10. M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Process. De Gruyter (1994). [Google Scholar]
  11. F. Flandoli and F. Russo, Generalized integration and stochastic ODEs. Ann. Probab. 30 (2002) 270–292. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Friz and N. Victoir, A note on the notion of geometric rough paths. To appear in Probab. Theory Related Fields (2006). [Google Scholar]
  13. B.M. Hambly and T.J. Lyons, Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab. 26 (1998) 132–148. [CrossRef] [MathSciNet] [Google Scholar]
  14. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes. North Holland, 2nd edition (1989). [Google Scholar]
  15. H. Kunita, Stochastic flows and stochastic differential equations. Cambridge University Press (1990). [Google Scholar]
  16. A. Lejay, Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme-divergence : cas linéaires et semi-linéaires. Ph.D. thesis, Université de Provence, Marseille, France (2000). www.iecn.u-nancy.fr/~lejay/. [Google Scholar]
  17. A. Lejay, An introduction to rough paths, in Séminaire de probabilités, XXXVII. Lect. Notes Math. 1832 (2003) 1–59, Springer, Berlin. [Google Scholar]
  18. A. Lejay, A Probabilistic Representation of the Solution of some Quasi-Linear PDE with a Divergence-Form Operator. Application to Existence of Weak Solutions of FBSDE. Stochastic Process. Appl. 110 (2004) 145–176. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Lejay, Stochastic Differential Equations driven by processes generated by divergence form operators II: Convergence results. Institut Élie Cartan de Nancy (preprint), 2003. [Google Scholar]
  20. A. Lejay and T.J. Lyons, On the Importance of the Lévy Area for Systems Controlled by Converging Stochastic Processes. Application to Homogenization, in New Trend in Potential Theory, D. Bakry, L. Beznea, Gh. Bucur and M. Röckner Eds., The Theta Foundation (2006). [Google Scholar]
  21. M. Ledoux, T. Lyons and Z. Qian, Lévy area of Wiener processes in Banach spaces. Ann. Probab. 30 (2002) 546–578. [CrossRef] [MathSciNet] [Google Scholar]
  22. T. Lyons and Z. Qian, System Control and Rough Paths. Oxford Mathematical Monographs. Oxford University Press (2002). [Google Scholar]
  23. T.J. Lyons and L. Stoica, The limits of stochastic integrals of differential forms. Ann. Probab. 27 (1999) 1–49. [CrossRef] [MathSciNet] [Google Scholar]
  24. T.J. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998) 215–310. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Lejay and N. Victoir, On (p,q)-rough paths. J. Differential Equations 225 (2006) 103–133. [CrossRef] [MathSciNet] [Google Scholar]
  26. Z. Ma and M. Röckner, Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Universitext. Springer-Verlag (1991). [Google Scholar]
  27. E.J. McShane. Stochastic differential equations and models of random processes. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, pp. 263–294. Univ. California Press (1972). [Google Scholar]
  28. A. Rozkosz, Stochastic Representation of Diffusions Corresponding to Divergence Form Operators. Stochastic Process. Appl. 63 (1996) 11–33. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Rozkosz, On Dirichlet processes associated with second order divergence form operators. Potential Anal. 14 (2001) 123–148. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Rozkosz and L. Slomiński, Extended Convergence of Dirichlet Processes. Stochastics Stochastics Rep. 65 (1998) 79–109. [MathSciNet] [Google Scholar]
  31. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Springer-Verlag (1990). [Google Scholar]
  32. E.-M. Sipiläinen, A pathwise view of solutions of stochastic differential equations. Ph.D. thesis, University of Edinburgh (1993). [Google Scholar]
  33. D.W. Stroock, Diffusion Semigroups Corresponding to Uniformly Elliptic Divergence Form Operator, in Séminaire de Probabilités XXII. Lect. Notes Math. 1321 (1988) 316–347. Springer-Verlag. [CrossRef] [Google Scholar]
  34. D.R.E. Williams, Path-wise solutions of SDE's driven by Lévy processes. Rev. Mat. Iberoamericana 17 (2002) 295–330. arXiv:math.PR/0001018. [Google Scholar]
  35. E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals. Ann. Math. Statist. 36 (1965) 1560–1564. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.