On uniformly subelliptic operators and stochastic area

Probability Theory and Related Fields

Volumn 142, Issue 3-4, 2008, Pages 475-523

  Friz, Peter ^a   Victoir, Nicolas ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49749103675     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0113-y     Document Type: Article

References (37)

1. D.G. Aronson 1967 Bounds for the fundamental solution of a parabolic equation Bull. Am. Math. Soc. 73 890 896
2. R.F. Bass T. Kumagai 2000 Laws of the iterated logarithm for some symmetric diffusion processes Osaka J. Math. 37 3 625 650
3. G.B. Arous M. Grǎdinaru M. Ledoux 1994 Hölder norms and the support theorem for diffusions Ann. Inst. H. Poincaré Probab. Stat. 30 3 415 436
4. E.A. Carlen S. Kusuoka D.W. Stroock 1987 Upper bounds for symmetric Markov transition functions Ann. Inst. H. Poincaré Probab. Stat. 23 2, suppl 245 287
5. Davies E.B. (1989). Heat Kernels and Spectral Theory, Vol. 92 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge
6. Dembo A. and Zeitouni O. (1998). Large Deviations Techniques and Applications, Vol. 38 of Applications of Mathematics (New York), Second edition. Springer, New York
7. Deuschel J.-D. and Stroock D.W. (1989). Large Deviations, Vol. 137 of Pure and Applied Mathematics. Academic, Boston
8. E.B. Fabes D.W. Stroock 1986 A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash Arch. Rational Mech. Anal. 96 4 327 338
9. P. Friz T. Lyons D. Stroock 2006 Lévy's area under conditioning Ann. Inst. H. Poincaré Probab. Stat. 42 1 89 101
10. P. Friz N. Victoir 2006 A note on the notion of geometric rough paths Probab. Theory Related Fields 136 395 416
11. Friz, P., Victoir, N.: Euler estimates for rough differential equations. J. Differ. Equ. (2007). doi: 10.1016/j.jde.2007.10.008
12. Fukushima M., Ōshima Y. and Takeda M. (1994). Dirichlet Forms and Symmetric Markov Processes, Vol. 19 of de Gruyter Studies in Mathematics. Walter de Gruyter, Berlin
13. Ikeda N. and Watanabe S. (1989). Stochastic Differential Equations and Diffusion Processes, Second edition. North-Holland, Amsterdam
14. D. Jerison 1986 The Poincaré inequality for vector fields satisfying Hörmander's condition Duke Math. J. 53 2 503 523
15. A. Lejay 2006 Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem ESAIM Probab. Stat. 10 356 379
16. Lejay, A.: Stochastic differential equations driven by processes generated by divergence form operators II: Convergence results. ESAIM Probab. Stat. (2007, accepted)
17. T. Lyons 1998 Differential equations driven by rough signals Rev. Mat. Iberoamericana 14 2 215 310
18. Lyons, T.: St. Flour Lectures on Rough Paths, 2004. Handwritten notes available at http://www.sag.maths.ox.ac.uk/tlyons/st-flour/
19. Lyons, T., Qian, Z.: System Control and Rough Paths. Oxford University Press, Oxford Mathematical Monographs, (2002)
20. T. Lyons L. Stoica 1999 The limits of stochastic integrals of differential forms Ann. Probab. 27 1 1 49
21. Millet, A., Sanz-Solé, M.: A simple proof of the support theorem for diffusion processes. In Séminaire de Probabilités, XXVIII, volume 1583 of Lecture Notes in Math., p. 36-48. Springer, Berlin, (1994)
22. Montgomery R. (2002). A tour of subriemannian geometries, their geodesics and applications, Vol. 91 of Mathematical Surveys and Monographs. American Mathematical Society, Providence
23. J. Moser 1971 On a pointwise estimate for parabolic differential equations Commun. Pure Appl. Math. 24 727 740
24. J. Moser 1964 A Harnack inequality for parabolic differential equations Commun. Pure Appl. Math. 17 101 134
25. J.A. Ramírez 2001 Short-time asymptotics in Dirichlet spaces Commun. Pure Appl. Math. 54 3 259 293
26. Robinson, D.W.: Elliptic Operators and Lie Groups. Oxford Mathematical Monographs. Clarendon, Oxford University Press, New York, 1991. Oxford Science Publications
27. L. Saloff-Coste D.W. Stroock 1991 Opérateurs uniformément sous-elliptiques sur les groupes de Lie J. Funct. Anal. 98 1 97 121
28. Stroock, D.W.: Diffusion semigroups corresponding to uniformly elliptic divergence form operators. In Séminaire de Probabilités, XXII, Vol. 1321 of Lecture Notes in Math., pp. 316-347. Springer, Berlin, (1988)
29. Stroock, D.W., Varadhan, S.R.S.: On the support of diffusion processes with applications to the strong maximum principle. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, CA, 1970/1971), Vol. III: Probability theory, pp. 333-359, Berkeley, 1972. University California Press
30. K.T. Sturm 1996 Analysis on local Dirichlet spaces. III. The parabolic Harnack inequality J. Math. Pures Appl. (9), 75 3 273 297
31. K.-T. Sturm 1995 Analysis on local Dirichlet spaces. II. Upper Gaussian estimates for the fundamental solutions of parabolic equations Osaka J. Math. 32 2 275 312
32. Sturm, K.-T.: On the geometry defined by Dirichlet forms. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993), volume 36 of Progr. Probab., pp. 231-242. Birkhäuser, Basel, (1995)
33. ter Elst, A.F.M., Robinson, D.W.: Second-order subelliptic operators on Lie groups. II. Real measurable principal coefficients. In Semigroups of operators: theory and applications (Newport Beach, CA, 1998), vol. 42 of Progr. Nonlinear Differential Equations Appl., pp. 103-124. Birkhäuser, Basel, (2000)
34. S.R.S. Varadhan 1967 Diffusion processes in a small time interval Commun. Pure Appl. Math. 20 659 685
35. Varadhan, S.R.S.: Lectures on diffusion problems and partial differential equations, Vol. 64 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics. Tata Institute of Fundamental Research, Bombay, 1980. With notes by Pl. Muthuramalingam and Tara R. Nanda
36. N.Th. Varopoulos 1990 Small time Gaussian estimates of heat diffusion kernels. II. The theory of large deviations J. Funct. Anal. 93 1 1 33
37. Varopoulos N.Th., Saloff-Coste L. and Coulhon T. (1992). Analysis and Geometry on Groups, Vol. 100 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge