On the Quasi-regularity of Semi-Dirichlet Forms

Potential Analysis

Volumn 15, Issue 3, 2001, Pages 151-185

  Fitzsimmons, P J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Continuous additive functional; Quasi continuous; Quasi regular; Right process; Semi Dirichlet form; Standard process; Tightness; Time change

Indexed keywords

EID: 0035635039     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011249920221     Document Type: Article

References (43)

1. Albeverio, S., Fan, R.-Z., Röckner, M. and Stannat, W.: 'A remark on coercive forms and associated semigroups'. In: Partial Differential Operators and Mathematical Physics (Holzhau, 1994), pp. 1-8. Oper. Theory Adv. Appl. 78, Birkhauser, Basel, 1995.
2. Albeverio, S., Fan, R.-Z., Röckner, M. and Stannat, W.: 'A remark on coercive forms and associated semigroups'. In: Partial Differential Operators and Mathematical Physics (Holzhau, 1994), pp. 1-8. Oper. Theory Adv. Appl. 78, Birkhauser, Basel, 1995.
3. Albeverio, S. and Ma, Z.-M.: 'A general correspondence between Dirichlet forms and right processes'. Bull. Amer. Math. Soc. 26 (1991), 245-252.
4. Albeverio, S. and Ma, Z.-M.: 'Necessary and sufficient conditions for the existence of m-perfect processes associated with Dirichlet forms'. In: Séminaire de probabilités XXV, Lecture Notes in Math. 1485 pp. 374-406. Springer-Verlag, Berlin, 1991.
5. Albeverio, S., Ma, Z.-M. and Röckner, M.: 'A remark on the support of cadlag processes', In: S. Cambanis et al. (eds), Stochastic Processes: A Festschrift in Honour of Gopinath Kallianpur, pp. 1-5. Springer-Verlag, New York, 1993.
6. Ancona, A.: 'Sur les espaces de Dirichlet: principes, fonctions de Green'. J. Math. Pures et Appl. 54 (1975), 75-124.
7. Blumenthal, R. M. and Getoor, R. K.: Markov Processes and Potential Theory. Academic Press, New York, 1968.
8. Bouleau, N. and Hirsch, F.: Dirichlet Forms and Analysis on Wiener Space. De Gruyter, Berlin, New York, 1991.
9. Carillo Menendez, S.: 'Processus de Markov associé à une forme de Dirichlet non symétrique'. Z. Wahrsch. verw. Geb. 33 (1975), 139-154.
10. Dellacherie, C. and Meyer, P.-A.: Probabilités et Potentiel, A, Ch. I à IV, Hermann, Paris, 1975.
11. Dong, Z. and Ma, Z.-M.: 'An integral representation theorem for quasi-regular Dirichlet spaces'. Chinese. Sci. Bull. 38 (1993), 1355-1358.
12. El Karoui, N.: Les aspects probabilstes du contrôle stochastique'. In: Ecole d'été de probabilités de St. Flour IX. Lecture Notes in Math. 876, pp. 74-239. Springer-Verlag, Berlin, 1981.
13. Fitzsimmons, P. J.: 'Markov processes and nonsymmetric Dirichlet forms without regularity', J. Func. Anal. 85 (1989), 287-306.
14. Fitzsimmons, P. J.: 'Time changes of symmetric Markov processes and a Feynman-Kac formula'. J. Theoret. Probab. 2 (1989), 487-501.
15. Fitzsimmons, P. J. and Getoor, R. K.: 'Revuz measures and time changes'. Math. Zeit. 199 (1988), 233-256.
16. Fitzsimmons, P. J. and Getoor, R. K.: 'On the potential theory of symmetric Markov processes'. Math. Annalen 281 (1988), 495-512.
17. Fitzsimmons, P. J. and Getoor, R. K.: 'Smooth measures and continuous additive functionals of right Markov processes'. In: N. Ikeda, S. Watanabe, M. Fukushima, H. Kunita (eds) Itô's Stochastic Calculus and Probability Theory, Springer, Tokyo, 1996, pp. 31-49.
18. Fukushima, M.: Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, Oxford, New York, 1980.
19. Fukushima, M., Oshima, Y. and Takeda, M.: Dirichlet Forms and Markov Processes. De Gruyter, Berlin, New York, 1994.
20. Getoor, R. K.: Markov Processes: Ray Processes and Right Processes. Lecture Notes in Math. 440. Springer-Verlag, Berlin, Heidelberg, New York, 1975.
21. Getoor, R. K.: 'Excursions of a Markow process'. Ann. Prob. 7 (1979), 244-266.
22. Getoor, R. K.: Transience and recurrence of Markov processes. Lecture Notes in Math. 784, pp. 397-409, Springer, Berlin, 1980.
23. Getoor, R. K. and Glover, J.: 'Markov processes with identical excessive measures'. Math. Zeit. 184 (1983), 287-300.
24. Getoor, R. K. and Sharpe, M. J.: 'Naturality, standardness, and weak duality for Markov processes'. Z. Wahrsch. verw. Geb. 67 (1984), 1-62.
25. Glover, J., Rao, M., Šikić, H. and Song, R.: 'Quadratic forms corresponds to the generalized Schrodinger semigroups', J. Funct. Anal. 125 (1994), 358-378.
26. Kato, T.: Perturbation Theory for Linear Opertors. Second edition. Grundlehren der Mathematischen Wissenschaften, Band 132. Springer-Verlag, Berlin, New York, 1976.
27. LeJan, Y.: 'Balayage et formes de Dirichlet'. Z. Wahrsch. verw. Geb. 37 (1977), 297-319.
28. Ma, Z.-M., Overbeck, L. and Röckner, M.: 'Markov processes associated with semi-Dirichlet forms'. Osaka J. Math. 32 (1994), 97-119.
29. Ma, Z.-M. and Röckner, M.: Introduction to the Theory of (Non-symmetric) Dirichlet forms. Springer-Verlag, Berlin, Heidelberg, New York, 1992.
30. Ma, Z.-M. and Röckner, M.: 'Markov processes associated with positivity preserving coercive forms'. Canad. J. Math. 47 (1995), 817-840.
31. Mertens, J.-F: 'Strongly supermedian functions and optimal stopping'. Z. Wahrsch. verw. Gebiete 26 (1973), 119-139.
32. Mosco, U.: 'Approximation of the solutions of some variational inequalities'. Ann. Sc. Norm. Sup. Pisa 21 (1967), 373-394.
33. Revuz, D.: 'Mesures associées aux fonctionelles additives de Markov, I'. Trans. Amer. Math. Soc. 148 (1970), 501-531.
34. Röckner, M. and Schmuland, B.: 'Quasi-regular Dirichlet forms: examples and counterexamples'. Canad. J. Math. 47 (1995), 165-200.
35. Sharpe, M. J.: General Theory of Markov Processes. Academic Press, San Diego, 1988.
36. Silverstein, M.: Symmetric Markov Processes. Lecture Notes in Math. 426, Springer-Verlag, Berlin, Heidelberg, New York, 1974.
37. Silverstein, M.: 'The sector condition implies that semipolar sets are quasi-polar'. Z. Wahrsch. verw. Geb. 41 (1977), 13-33.
38. Silverstein, M.: 'Application of the sector condition to the classification of subMarkovian semigroups'. Trans. Amer. Math. Soc. 244 (1998), 103-146.
39. Stampacchia, G.: 'Formes bilinéaires coercitives sur les ensembles convexes', C. R. Acad. Sc. Paris, Sér. A-B, 258 (1964), 4413-4416.
40. Stannat, W.: 'Generalized Dirichlet forms and associated Markov processes'. C. R. Acad. Sc. Paris, Sér. I, 319 (1994), 1063-1068.
41. Stollmann, P.: 'Closed ideas in Dirichlet spaces'. Potential Analysis 2 (1993), 263-268.
42. Stollmann, P. and Voigt, J.: 'Perturbation of Dirichlet forms by measures'. Potential Anal. 5 (1996), 109-138.
43. Ying, J.: 'Bivariate Revuz measures and the Feyman-Kac formula'. Ann. Inst. Henri Poincaré, Probab. Statist. 32 (1995), 251-287.