Girsanov and Feynman-Kac type transformations for symmetric Markov processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, p. 475-505
@article{AIHPB_2002__38_4_475_0,
     author = {Chen, Zhen-Qing and Zhang, Tu-Sheng},
     title = {Girsanov and Feynman-Kac type transformations for symmetric Markov processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {38},
     number = {4},
     year = {2002},
     pages = {475-505},
     zbl = {1004.60077},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_4_475_0}
}
Chen, Zhen-Qing; Zhang, Tu-Sheng. Girsanov and Feynman-Kac type transformations for symmetric Markov processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, pp. 475-505. http://www.numdam.org/item/AIHPB_2002__38_4_475_0/

[1] S. Albeverio, Z.-M. Ma, Perturbation of Dirichlet forms-lower semiboundedness, closability, and form cores, J. Funct. Anal. 99 (1991) 332-356. | MR 1121617 | Zbl 0743.60071

[2] S. Albeverio, M. Röckner, T. Zhang, Girsanov transform for symmetric diffusion with infinite dimensional state space, Ann. Probab. 21 (1993) 961-978. | MR 1217575 | Zbl 0776.60093

[3] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR 264757 | Zbl 0169.49204

[4] Z.-Q. Chen, Z.-M. Ma, M. Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya Math. J. 136 (1994) 1-15. | MR 1309378 | Zbl 0811.31002

[5] K.L. Chung, Z. Zhao, From Brownian Motion to Schrödinger's Equation, Springer, New York, 1995. | MR 1329992 | Zbl 0819.60068

[6] C. Dellacherie, P.-A. Meyer, Probabilités et Potentiel, Chapites V à VIII, Hermann, 1980. | MR 566768 | Zbl 0464.60001

[7] S.N. Either, T.G. Kurtz, Markov Processes-Characterization and Convergence, Wiley, New York, 1986. | MR 838085 | Zbl 0592.60049

[8] P.J. Fitzsimmons, Even and odd continuous additive functionals, in: Dirichlet Forms and Stochastic Processes, De Gruyter, Berlin, 1988, pp. 139-154. | MR 1366430 | Zbl 0844.60048

[9] P.J. Fitzsimmons, Absolute continuity of symmetric diffusions, Ann. Probab. 25 (1997) 230-258. | MR 1428508 | Zbl 0873.60054

[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. Poincarè 28 (1992) 311-333. | Numdam | MR 1162577 | Zbl 0749.60072

[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. | MR 661622 | Zbl 0485.60075

[12] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. | MR 1303354 | Zbl 0838.31001

[13] M. Fukushima, M. Takeda, A transformation of symmetric Markov processes and the Donsker-Varadhan theory, Osaka J. Math. 21 (1984) 311-326. | Zbl 0542.60077

[14] J. Glover, M. Rao, H. Sikic, R. Song, Quadratic forms corresponding to the generalized Schrödinger semigroups, J. Funct. Anal. 125 (1994) 358-378. | MR 1297672 | Zbl 0807.60056

[15] S.W. He, J.G. Wang, J.A. Yan, Semimartingale Theory and Stochastic Calculus, Science Press, Beijing, 1992. | MR 1219534 | Zbl 0781.60002

[16] H. Kunita, Absolute continuity of Markov processes, in: Seminaire de Probabilites X, Lect. Notes Math., 511, 1976, pp. 44-77. | Numdam | MR 438489 | Zbl 0438.60033

[17] Z.-M. Ma, M. Röckner, Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer, Berlin, 1992. | Zbl 0826.31001

[18] S. Orey, Conditions for the absolute continuity of two diffusions, Trans. Amer. Math. Soc. 193 (1974) 413-426. | MR 370794 | Zbl 0303.60071

[19] Y. Oshima, On absolute continuity of two symmetric diffusion processes, in: Lect. Notes Math., 1250, Springer, Berlin, 1987, pp. 184-194. | MR 897808 | Zbl 0619.60070

[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. | MR 897807 | Zbl 0634.60064

[21] M. Sharpe, General Theory of Markov Processes, Academic Press, 1988. | MR 958914 | Zbl 0649.60079

[22] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982) 447-526. | MR 670130 | Zbl 0524.35002

[23] M. Takeda, Topics on Dirichlet forms and symmetric Markov processes, Sugaku Expositions 12 (1999) 201-222. | MR 1723167 | Zbl 1013.31006

[24] M. Takeda, T. Zhang, Asymptotic properties of additive functionals of Brownian motion, Ann. Probab. 25 (1997) 940-952. | MR 1434132 | Zbl 0887.60077

[25] T. Zhang, Generalized Feynman-Kac semigroups, associated quadratic forms and asymptotic properties, Preprint, 1998, To appear in Potential Analysis. | Zbl 0984.31006

[26] T. Yamada, On the fractional derivative of Brownian local time, J. Math. Kyoto Univ. 25 (1985) 49-58. | MR 777245 | Zbl 0625.60090

[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. | MR 849222 | Zbl 0618.60080

[28] Z. Zhao, A probabilistic principle and generalized Schrödinger perturbation, J. Funct. Anal. 101 (1991) 162-176. | MR 1132313 | Zbl 0748.60069