Exponential Decay of Lifetimes and a Theorem of Kac on Total Occupation Times

Potential Analysis

Volumn 11, Issue 3, 1999, Pages 235-247

  Takeda, Masayoshi ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Additive functional; Dirichlet form; Exponenial decay of lifetime; Large deviation; Time change

Indexed keywords

EID: 0033444868     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008649623291     Document Type: Article

References (18)

1. Albeverio, S., Blanchard, P. and Ma, Z. M.: 'Feynmann-Kac semigroups in terms of signed smooth measures', Random Partial Differential Equations, (eds.) U. Hornung et al., Birkhäuser, 1989.
2. Albeverio, S. and Ma, Z. M.: 'Perturbation of Dirichlet forms - Lower boundedness, closability, and form cores', J. Funct. Anal. 99, 332-356 (1991).
3. Brasche, J., Exner, P., Kuperin, Yu. and Seba, P.: 'Schrödinger operators with singular interactions', J. Math. Anal. Appl. 184, 112-139 (1994).
4. Chung, K. L. and Zhao, Z.: From Brownian Motion to Schrödinger's Equation, Springer, Berlin, Heidelberg, New York, 1995.
5. 1 properties of second order elliptic operators', Bull. London Math. Soc. 17, 417-436 (1985).
6. Davies, E. B.: Heat Kernels and Spectral Theory, Cambridge, Cambridge, 1989.
7. Donsker, M. D. and Varadhan, S. R. S.: 'Asymptotic evaluation of certain Wiener integrals for large time', Proceedings of International Conference on Function Space, (ed.) A. M. Arthure, Oxford, 1974.
8. Fitzsimmons, P. J. and Getoor, R. K.: 'On the potential theory of symmetric Markov processes', Math. Ann. 281, 495-512 (1988).
9. Fukushima, M., Oshima, Y. and Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994.
10. Kac, M.: 'On some connections between probability theory and differential equations', Proc. 2nd Berk. Symp. Math. Statist. Probability, 189-215 (1950).
11. Kawabata, T. and Takeda, M.: 'On uniqueness problem for local Dirichlet forms', Osaka J. Math. 33, 881-893 (1996).
12. Maz'ja, V. G.: Sobolev Spaces, Springer, Berlin, Heidelberg, New York, 1985.
13. McKean, H. P.: Stochastic Integrals, Academic Press, New York, 1969.
14. Rogers, L. C. G. and Williams, D.: Diffusions, Markov Processes, and Martingale, Vol I, Wiley, New York, 1994.
15. Sharpe, M.: General Theory of Markov Processes, Academic Press, New York, 1988.
16. Stollmann, P. and Voigt, V.: 'Perturbation of Dirichlet forms by measures', preprint, Potential Analysis 5, 109-138 (1996).
17. p-Liouville properties', J. Reine Angew. Math. 456, 173-196 (1994).
18. Takeda, M.: 'A large deviation for symmetric Markov processes with finite lifetime', Stochastics and Stochastic Reports 59, 143-167 (1996).