Asymptotic Properties of Generalized Feynman-Kac Functionals

Potential Analysis

Volumn 9, Issue 3, 1998, Pages 261-291

  Takeda, Masayoshi ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Dirichlet forms; Generalized Feynman Kac formula; Symmetric Markov processes

Indexed keywords

EID: 0032280470     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008656907265     Document Type: Article

References (30)

1. Albeverio, S., Blanchard, P. and Ma, Z. M.: 'Feynman-Kac semigroups in terms of signed smooth measures', in U. Hornung et al. (eds.), Random Partial Differential Equations, Birkhöuser, 1991.
2. Albeverio, S., Gesztesy, F., Hoegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics, Springer, 1988.
3. Albeverio, S. and Ma, Z. M.: 'Perturbation of Dirichlet forms - Lower boundedness, closability, and form cores', J. Funct. Ananl. 99 (1991), 332-356.
4. Antonie, J. P., Gesztesy, F. and Shabani, J.: 'Exactly solvable models of sphere interactions in quantum mechanics', J. Phys. A20 (1987), 3687-3712.
5. Biroli, M. and Mosco, U.: 'Formes de Dirichlet et estimations structurelles dans les millieux discontinuous', C. R. Acad. Sci. Paris 313 (1991), 593-598.
6. Blanchard, P. and Ma, Z. M.: 'Semigroup of Schrödinger operators with potentials given by Radon measures', in S. Albeverio et al. (eds.), Stochastic Processes - Physics and Geometry, World Scient., Singapore, 1990.
7. Brasche, J., Exner, P., Kuperin, Yu. and Seba, P.: 'Schrödinger operators with singular interactions', J. Math. Anal. Appl. 184 (1994), 112-139.
8. Carmona, R., Masters, W. C. and Simon, B.: 'Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions', J. Funct. Anal. 91 (1990), 117-142.
9. Chung, K. L.: 'Doubly-Feller process with multiplicative functional', Seminar on Stochastic Processes, Birkhäuser (1986), 63-78.
10. Chung, K. L. and Getoor, R. K.: 'The condenser problem', Ann. Prob. 5 (1986), 82-86.
11. Davies, E. B.: Heat Kernels and Spectral Theory, Cambridge, 1989.
12. Donsker, M. D. and Varadhan, S. R. S.: 'Asymptotic evaluation of certain Wiener integrals for large time', Proceedings of International Conference on Function Space, A. M. Arthure (ed.), Oxford, 1974.
13. Donsker, M. D. and Varadhan, S. R. S.: 'Asymptotic evaluation of certain Markov process expectations for large time I', Comm. Pure Appl. Math. 28 (1975), 1-47.
14. Donsker, M. D. and Varadhan, S. R. S.: 'Asymptotic evaluation of certain Markov process expectations for large time III', Comm. Pure Appl. Math. 29 (1976), 389-461.
15. Fukushima, M.: 'A note on irreducibility and ergodicity of symmetric Markov processes', Springer Lecture Notes in Physics 173 (1982).
16. Fukushima, M., Oshima, Y. and Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter, 1994.
17. Kac, M.: 'On some connections between probability theory and differential equations', Proc. 2nd Berk. Symp. Math. Statist. Probability (1950), 189-215.
18. Ma, Z. M. and Röckner, M.: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer, 1992.
19. Sharpe, M.: General Theory of Markov Processes, Academic Press, 1988.
20. Simon, B.: 'A canonical decomposition for quadratic forms with applications to monotone convergence theorems', J. Funct. Anal. 28 (1978), 377-385.
21. Simon, B.: 'Schrödinger semigroups', Bull. Am. Math. Soc. 7 (1982), 447-536.
22. Stollmann, P. and Voigt, V: 'Perturbation of Dirichlet forms be measures', Potential Analysis 5 (1996), 109-138.
23. Stroock, D.: Probability Theory, An Analytic View, Cambridge, 1993.
24. Sturm, K. T.: 'Schrödinger operators and Feynman-Kac semigroups with arbitrary nonnegative potentials', Expo. Math. 12 (1994), 385-411.
25. Sturm, K. T.: 'Schrödinger semigroups on manifolds', J. Funct. Anal. 118 (1993), 309-350.
26. p-spectrum of uniformly elliptic operators on Riemannian manifolds', J. Funct. Anal. 118 (1993), 442-453.
27. p-Liouville properties', J. reine angew. Math. 456 (1994), 173-196.
28. Sturm, K. T.: 'Analysis on local Dirichlet space - II. Gaussian upper bounds for fundamental solutions of parabolic equations', Osaka J. Math. 32 (1995), 275-312.
29. Sturm, K. T.: 'On the geometry defined by Dirichlet forms, Seminer on Stochastic Analysis, Randam Fields and Applications', Bolthausen, (ed.), Progress in Probability 36, Birkhäuser (1995), 231-242.
30. Takeda, M.: 'A large deviation for symmetric Markov processes with finite life time', Stochastics and Stochastic Reports 59 (1996), 143-167.