Girsanov and Feynman–Kac type transformations for symmetric Markov processes

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1. [1] S. Albeverio, Z.-M. Ma, Perturbation of Dirichlet forms-lower semiboundedness, closability, and form cores, J. Funct. Anal.99 (1991) 332-356. Zbl0743.60071MR1121617
2. [2] S. Albeverio, M. Röckner, T. Zhang, Girsanov transform for symmetric diffusion with infinite dimensional state space, Ann. Probab.21 (1993) 961-978. Zbl0776.60093MR1217575
3. [3] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. Zbl0169.49204MR264757
4. [4] Z.-Q. Chen, Z.-M. Ma, M. Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya Math. J.136 (1994) 1-15. Zbl0811.31002MR1309378
5. [5] K.L. Chung, Z. Zhao, From Brownian Motion to Schrödinger's Equation, Springer, New York, 1995. Zbl0819.60068MR1329992
6. [6] C. Dellacherie, P.-A. Meyer, Probabilités et Potentiel, Chapites V à VIII, Hermann, 1980. Zbl0464.60001MR566768
7. [7] S.N. Either, T.G. Kurtz, Markov Processes-Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
8. [8] P.J. Fitzsimmons, Even and odd continuous additive functionals, in: Dirichlet Forms and Stochastic Processes, De Gruyter, Berlin, 1988, pp. 139-154. Zbl0844.60048MR1366430
9. [9] P.J. Fitzsimmons, Absolute continuity of symmetric diffusions, Ann. Probab.25 (1997) 230-258. Zbl0873.60054MR1428508
10. [10] P.J. Fitzsimmons, R.K. Getoor, Limit theorems and variation properties for fractional derivatives of the local time of a stable processes, Ann. Inst. Henri. Poincarè28 (1992) 311-333. Zbl0749.60072MR1162577
11. [11] M. Fukushima, On absolute continuity of multi-dimensional symmetrizalle diffusion, in: Functional Analysis in Markov Processes, Lect. Notes Math., 923, 1982, pp. 146-176. Zbl0485.60075MR661622
12. [12] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. Zbl0838.31001MR1303354
13. [13] M. Fukushima, M. Takeda, A transformation of symmetric Markov processes and the Donsker–Varadhan theory, Osaka J. Math.21 (1984) 311-326. Zbl0542.60077
14. [14] J. Glover, M. Rao, H. Sikic, R. Song, Quadratic forms corresponding to the generalized Schrödinger semigroups, J. Funct. Anal.125 (1994) 358-378. Zbl0807.60056MR1297672
15. [15] S.W. He, J.G. Wang, J.A. Yan, Semimartingale Theory and Stochastic Calculus, Science Press, Beijing, 1992. Zbl0781.60002MR1219534
16. [16] H. Kunita, Absolute continuity of Markov processes, in: Seminaire de Probabilites X, Lect. Notes Math., 511, 1976, pp. 44-77. Zbl0438.60033MR438489
17. [17] Z.-M. Ma, M. Röckner, Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer, Berlin, 1992. Zbl0826.31001
18. [18] S. Orey, Conditions for the absolute continuity of two diffusions, Trans. Amer. Math. Soc.193 (1974) 413-426. Zbl0303.60071MR370794
19. [19] Y. Oshima, On absolute continuity of two symmetric diffusion processes, in: Lect. Notes Math., 1250, Springer, Berlin, 1987, pp. 184-194. Zbl0619.60070MR897808
20. [20] Y. Oshima, M. Takeda, On a transformation of symmetric Markov processes and recurrence property, in: Lect. Notes Math., 1250, Springer, Berlin, 1987, pp. 171-183. Zbl0634.60064MR897807
21. [21] M. Sharpe, General Theory of Markov Processes, Academic Press, 1988. Zbl0649.60079MR958914
22. [22] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc.7 (1982) 447-526. Zbl0524.35002MR670130
23. [23] M. Takeda, Topics on Dirichlet forms and symmetric Markov processes, Sugaku Expositions12 (1999) 201-222. Zbl1013.31006MR1723167
24. [24] M. Takeda, T. Zhang, Asymptotic properties of additive functionals of Brownian motion, Ann. Probab.25 (1997) 940-952. Zbl0887.60077MR1434132
25. [25] T. Zhang, Generalized Feynman–Kac semigroups, associated quadratic forms and asymptotic properties, Preprint, 1998, To appear in Potential Analysis. Zbl0984.31006
26. [26] T. Yamada, On the fractional derivative of Brownian local time, J. Math. Kyoto Univ.25 (1985) 49-58. Zbl0625.60090MR777245
27. [27] T. Yamada, On some limit theorems for occupation times of one dimensional Brownian motion and its continuous additive functionals locally of zero energy, J. Math. Kyoto Univ.26 (1986) 309-322. Zbl0618.60080MR849222
28. [28] Z. Zhao, A probabilistic principle and generalized Schrödinger perturbation, J. Funct. Anal.101 (1991) 162-176. Zbl0748.60069MR1132313