Time changes of symmetric diffusions and Feller measures

Annals of Probability

Volumn 32, Issue 4, 2004, Pages 3138-3166

  Fukushima, Masatoshi ^a   He, Ping ^b   Ying, Jiangang ^c  

^a KANSAI UNIVERSITY   (Japan)

^b SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^c FUDAN UNIVERSITY   (China)

Author keywords

Dirichlet form; Douglas integral; Energy functional; Excursion; Feller measure; L vy system; Lipschitz domain; Symmetric diffusion; Time change

Indexed keywords

EID: 8744271490     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000649     Document Type: Article

References (22)

1. AIZENMAN, M. and SIMON, B. (1982). Brownian motion and Harnack's inequality for Schrödinger operators. Comm. Pure Appl. Math. 35 209-271.
2. BASS, R. F. and BURDZY, K. (1990). A probabilistic proof of the boundary Harnack principle. In Seminar on Stochastic Processes 1989 (E. Çinlar, K. L. Chung, R. Getoor, P. J. Fitzsimmons and R. J. Williams, eds.) 1-16. Birkhäuser, Boston.
3. CHEN, Z. Q. (1992). On reflected Dirichlet spaces. Probab. Theory Related Fields 94 135-162.
4. DOOB, J. L. (1962). Boundary properties of functions with finite Dirichlet integrals. Ann. Inst. Fourier 12 573-621.
5. DOOB, J. L. (1984). Classical Potential Theory and Its Probabilistic Counterpart. Springer, Berlin.
6. DOUGLAS, J. (1931). Solution of the problem of Plateau. Trans. Amer. Math. Soc. 33 263-321.
7. FELLER, W. (1957). On boundaries and lateral conditions for the Kolmogorov differential equations. Ann. of Math. 65 527-570.
8. FUKUSHIMA, M. (1964). On Feller's kernel and the Dirichlet norm. Nagoya Math. J. 24 167-175.
9. FUKUSHIMA, M. (1969). On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities. J. Math. Soc. Japan 21 58-93.
10. FUKUSHIMA, M. (1999). On semimartingale characterizations of functionals of symmetric Markov processes. Electron. J. Probab. 4 1-32. Available at www.math.washington.edu/~ejpecp.
11. FUKUSHIMA, M., OSHIMA, Y. and TAKEDA, M. (1994). Dirichlet Forms and Symmetric Markov Processes. de Gruyter, Berlin.
12. FUKUSHIMA, M. and UEMURA, T. (2003). Capacitary bounds for measures and ultracontractivity of time changed processes. J. Math. Pures Appl. 82 553-572.
13. GETOOR, R. K. (1990). Excessive Measures. Birkhäuser, Boston.
14. HSU, P. (1986). On excursions of reflecting Brownian motion. Trans. Amer. Math. Soc. 296 239-264.
15. HUNT, R. R. and WHEEDEN, R. L. (1970). Positive harmonic functions on Lipschitz domains. Trans. Amer. Math. Soc. 147 507-527.
16. MA, Z. M. and RÖCKNER, M. (1992). Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Springer, Berlin.
17. NEVEU, J. (1961). Une generalisation des processus à accroissements positifs independents. Abh. Math. Sem. Univ. Hamburg 36-61.
18. SHARPE, M. J. (1988). General Theory of Markov Processes. Academic, San Diego.
19. SILVERSTEIN, M. L. (1974). The reflected Dirichlet space. III. Illinois J. Math. 18 310-355.
20. SILVERSTEIN, M. L. (1974). Symmetric Markov Processes. Lecture Notes in Math. 426 Springer, Berlin.
21. SILVERSTEIN, M. L. (1976). Boundary Theory for Symmetric Markov Processes. Lecture Notes in Math. 516. Springer, Berlin.
22. TAKEDA, M. (1996). Two classes of extensions for generalized Schrödinger operators. Potential Anal. 5 1-13.