On conservation of probability and the Feller property

Annals of Probability

Volumn 24, Issue 1, 1996, Pages 280-292

  Qian, Zhongmin ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Comparison theorem; Conservation; Diffusion; Feller property; Modified Ricci curvature

Indexed keywords

EID: 0030486557     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1042644717     Document Type: Article

References (18)

1. AZENCOTT, R. (1974). Behavior of diffusion semigroups at infinity. Bull. Soc. Math. France 102 193-240.
2. BAKRY, D. (1986). Un critère de non-explosion pour certaines diffusions sur une variété Riemannienne complète. C. R. Acad. Sci. Paris Sér. I Math. 303 23-26.
3. BAKRY, D. and EMERY, M. (1985). Diffusions hypercontractive. Séminaire de Probabilités XIX. Lecture Notes in Math. 1123 411-433. Springer, Berlin.
4. CHAVEL, I. (1984). Eigenvalues in Riemannian Geometry. Academic Press, New York.
5. DAVIES, E. B. (1992). Heat kernel bounds, conservation of probability and the Feller property. J. Anal. Math. 58 99-119.
6. 0-diffusion property. Stochastics 6 233-238.
7. GAFFNEY, M. P. (1959). The conservation property of the heat equation on Riemannian manifolds. Comm. Pure Appl. Math. 12 1-11.
8. GREENE, R. E. and WU, H. (1979). Function Theory on Manifolds Which Possess a Pole. Lecture Notes in Math. 699. Springer, Berlin.
9. GRIGOR'YAN, A. A. (1987). On stochastically complete Riemannian manifolds. Sov. Math. Dokl. 34 310-313.
10. HSU, P. (1989). Heat semigroup on a complete Riemannian manifold. Ann. Probab. 17 1248-1254.
11. ICHIHARA, K. (1986). Explosion problems for symmetric diffusion processes. Trans. Amer. Math. Soc. 298 515-536.
12. IKEDA, N. and WATANABE, S. (1981). Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.
13. KARP, L. and LI, P. (1982). The heat equation on complete Riemannian manifolds. Unpublished manuscript.
14. KENDALL, W. S. (1987). The radial part of Brownian motion on a manifold: a semimartingale property. Ann. Probab. 15 1491-1500.
15. LI, X. M. (1994). Strong p-completeness and the existence of smooth flows on noncompact manifolds. Probab. Theory Related Fields 104 485-511.
16. QIAN, Z. (1993). On Bakry-Emery's curvature dimension inequality and applications. Preprint, Univ. Warwick.
17. TAKEDA, M. (1991). The conservation property for the Brownian motion on Riemannian manifolds. Bull. London Math. Soc. 23 86-88.
18. YAU, S. T. (1978). On the heat kernel of a complete Riemannian manifold. J. Math. Pures Appl. 57 191-201.