The limits of stochastic integrals of differential forms

Annals of Probability

Volumn 27, Issue 1, 1999, Pages 1-49

  Lyons, Terry ^a   Stoica, Lucreţiu ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Dirichlet process; Lyons Zheng decomposition; Martingale decomposition; Path integral; Singular integral; Stochastic integral

Indexed keywords

EID: 0033243128     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022677253     Document Type: Article

References (22)

1. BLIEDTNER, J. and HANSEN, W. (1986). Potential Theory. Springer, New York.
2. BLUMENTHAL, R. M. and GETOOR, R. K. (1986). Markov Processes and Potential Theory. Academic Press, New York.
3. CONSTANTINESCU, C. and CORNEA, A. (1972). Potential Theory on Harmonic Spaces Springer, New York.
4. COURRÈGE, PH. and PRIOURET, P. (1965). Recollements de processus de Markov. Publ. Inst. Statist. Univ. Paris 14 275-377.
5. FABES, E. and STROOCK, D. (1986). A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Rational Mech. Anal. 96 327-338.
6. FUKUSHIMA, M., OSHIMA, Y. and TAKEDA, M. (1994). Dirichlet Forms and Symmetric Markov Processes. de Gruyter, Berlin.
7. GILBARG, D. and TRUDINGER, N. S. (1983). Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
8. LADYZENSKAYA, O. A., URALTSEVA, N. N. and SOLONIKOV, V. A. (1867). Linear and Quasilinear Equations of Parabolic Type. Nauka, Moskow. (In Russian.)
9. LI, P. and KARP, L. (1998). The heat equation on ccmplete Riemannian manifolds. Unpublished manuscript.
10. LI, P. and YAU, S. T. (1986). On the upper estimate of the heat kernel of a complete Riemannian manifold. Acta Math. 156 153-201.
11. LYONS, T. (1998). Random thoughts on reversible potential theory. Unpublished manuscript.
12. LYONS, T. and STOICA, L. (1996). On the limit of stochastic integrals of differential forms. Stochastics Monogr. 10. Gordon and Breach, Yverdon.
13. LYONS, T. J. and ZHANG, T. S. (1994). Decomposition of Dirichlet processes and its application. Ann. Probab. 22 1-26.
14. LYONS, T. J. and ZHENG, W. (1988). A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Astérisque 157-158 249-271.
15. LYONS, T. J. and ZHENG, W. A. (1990). On conditional diffusion processes. Proc. Roy. Soc. Edinburgh Sec. A 115 243-255.
16. MA, Z. M. and RÖCKNER, M. (1992). Introduction to the Theory of Dirichlet Forms. Springer, New York.
17. PRAT, J.-J. (1971). Étude asymptotique du mouvement brownian sur une variété riemannienne à courbure négative. C.R. Acad. Sci. Paris Sér. A 272 1586-1589.
18. SALOFF-COSTE, L. (1992). Uniformly elliptic operators on Riemannian manifolds. J. Diff. Geometry 36 417-450.
19. STOICA, L. (1980). Local Operators and Markov Processes. Lecture Notes in Math. 816, Springer, Berlin.
20. STROOCK, D. W. (1988). Diffusion semigroups corresponding to uniformly elliptic divergence form operators. Seminaire de Probabilités XXII Lecture Notes in Math. 1321 316-347. Springer, Berlin.
21. SULLIVAN, D. (1983). The Dirichlet problem at inf nity for a negatively curved manifold. J. Diff. Geometry 18 723-732.
22. TAKEDA, M. (1991). On the conservatineness of the Brownian motion on a Riemannian manifold. Bull. London Math. Soc. 23 86-88.