Formulae for the derivatives of heat semigroups

Journal of Functional Analysis

Volumn 125, Issue 1, 1994, Pages 252-286

  Elworthy, K D ^a   Li, X M ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000031706     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1006/jfan.1994.1124     Document Type: Article

References (19)

1. J. Bismut, “Large Deviations and the Malliavin Calculus,” Birkhauser, Basel, 1984.
2. P. R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Fund. Anal. 12 (1973), 401-414.
3. G. DaPrato, D. Elworthy, and J. Zabczyk, Strong Feller property for stochastic semi- linear equations, Warwick prepints, Jan. 1992; Stochastic Anal. Appl., to appear.
4. R. Elliott and M. Kohlmann, Integration by parts, homogeneous chaos expansions and smooth densities, Ann. Probab. 17, No. 1 (1989), 194-207.
5. K. D. Elworthy, Geometric aspects of diffusions on manifolds, in “Ecole d’été de probabilités de Saint-Flour XV-XVII, 1985, 1987” (P. L. Hennequin, Ed.), Lecture Notes in Mathematics, Vol. 1362, pp. 276-425, Springer-Verlag, New York/Berlin, 1988.
6. K. D. Elworthy, Stochastic flows on Riemannina manifolds, in "Diffusion Processes and Related Problems in Analysis” (M. A. Pinsky and V. Wihstutz, Eds.), Vol. II, pp. 37-72, Birkhäuser, Basel, 1992.
7. K. D. Elworthy and M. Yor, Conditional expectations for derivatives of certain stochastic flows, in “Seminaire de Probabilites XXVII” (J. Azéma, P. A. Meyer, and M, Yor, Eds), Lecture Notes in Math., Vol. 1557, pp. 159-172, Springer-Verlag, New York/Berlin, 1993.
8. K. D. Elworthy, “Stochastic Differential Equations on Manifold,” Cambridge Lecture Notes Series, Vol. 70, Cambridge Univ. Press, London/New York, 1982.
9. M. Freidlin, “Functional Integration and Partial Differential Equations,” Princeton Univ. Press, Princeton, NJ, 1985.
10. N. Ikeda and S. Watanabe, “Stochastic Differential Equations and Diffusion Processes,” 2nd ed., North-Holland, Amsterdam, 1989.
11. N. V. Krylov, Quasiderivatives for solutions of Ito’s stochastic equations and their applications, preprint.
12. X. M. Li, Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences. Warwick Preprints, No. 15, 1994, Probab. Theory Relat. Fields, to appear.
13. X.-M. Li, Strong p-completeness and the existence of smooth (lows on noncompact manifolds, Warwick preprints, No. 28, 1993, Probab. Theory Relat. Fields, to appear.
14. X.-M. Li, “Stochastic Flows on Noncompact Manifolds," Ph.D. thesis, 1992.
15. X.-M. Li and H. Z. Zhao, The existence of smooth solutions to reaction-diffusion equations and the smooth convergence of the travelling waves, manuscript.
16. J. Norris, Path integral formulae for heat kernels and their derivatives, Probab. Theory Related Fields 94 (1993), 525-541.
17. S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Polish Academy of Sciences, preprint, 1993.
18. L. Schwartz, “Théorie des distributions,” Hermann, Paris, 1966.
19. S. Watanabe, “Lectures on Stochastic Differential Equations and Malliavin Calculus, Tata Institute of Fundamental Research, Bombay,” Springer-Verlag, New York/Berlin, 1984.