Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

Journal of Functional Analysis

Volumn 230, Issue 2, 2006, Pages 382-418

  Kolesnikov, Alexander V ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Convergence of stochastic processes; Dirichlet forms; Gaussian measures; Gibbsian measures; Mosco convergence

Indexed keywords

EID: 29144468602     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.06.002     Document Type: Article

References (41)

1. S. Albeverio Yu.G. Kondratiev M. Röckner Dirichlet operators via stochastic analysis J. Funct. Anal. 128 1995 102-138
2. S. Albeverio Yu.G. Kondratiev M. Röckner Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states J. Funct. Anal. 149 1997 415-469
3. S. Albeverio Yu.G. Kondratiev M. Röckner T.V. Tsikalenko A priori estimates for symmetrizing measures and their applications to Gibbs states J. Funct. Anal. 171 2000 366-400
4. S. Albeverio S. Kusuoka L. Streit Convergence of Dirichlet forms and associated Schrödinger operators J. Funct. Anal. 68 1986 130-148
5. S. Albeverio M. Röckner Classical Dirichlet forms on topological vector spaces-closability and a Cameron-Martin formula J. Funct. Anal. 88 1990 395-436
6. V.I. Bogachev Differentiable measures and the Malliavin calculus J. Math. Sci. 87 5 1997 3577-3731
7. V.I. Bogachev Gaussian Measures 1998 American Mathematical Society Rhode Island
8. M. Briane N. Tchou Fibered microstructures for some nonlocal Dirichlet forms Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 2001 681-711
9. M. Camar-Eddine P. Seppecher Closure of the set of diffusion functionals with respect to the Mosco-convergence Math. Models Methods Appl. Sci. 12 8 2002 1153-1176
10. P. Cattiaux M. Fradon Entropy, reversible diffusion processes and Markov uniqueness J. Funct. Anal. 138 1996 243-272
11. G. Dal Maso An introduction to Γ -convergence Progress in Nonlinear Differential Equations and their Applications vol. 8 1993 Birkhäuser, Boston, Inc. Boston, MA
12. A. Eberle Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators, Lecture Notes in Mathematics vol. 1718 1999 Springer Berlin
13. L.S. Evans R.F. Gariepy Measure Theory and Fine Properties of Functions 1992 CRC Press Boca Raton, New York, Tokyo
14. M. Fukushima BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space J. Funct. Anal. 174 2000 227-249
15. M. Fukushima M. Hino On the space of BV functions and a related stochastic calculus in infinite dimensions J. Funct. Anal. 183 2001 245-268
16. M. Fukushima Y. Oshima M. Takeda Dirichlet Forms and Symmetric Markov Processes 1994 De Greyter Berlin
17. H.-O. Georgii Gibbs measures and phase transitions Studies in Mathematics vol. 9 1988 De Greyter Berlin, New York
18. M. Hino Convergence of non-symmetric forms J. Math. Kyoto Univ. 38 2 1998 329-341
19. d Forum. Math. 17 2005 225-259
20. K. Kuwae T. Shioya Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry Comm. Anal. Geom. 11 4 2003 599-673
21. K. Kuwae T. Uemura Weak convergence of symmetric diffusion processes II Proceedings of the 7th Japan-Russia Symposium on Probability Theory and Mathematical Statistics 1996 World Scientific 256-265
22. K. Kuwae T. Uemura Weak convergence of symmetric diffusion processes Probab. Theory Relat. Fields 109 1997 159-182
23. T.J. Lyons T.S. Zhang Note on convergence of Dirichlet processes Bull. London Math. Sci. 25 1993 353-356
24. T.J. Lyons T.S. Zhang Convergence of non-symmetric Dirichlet processes Stoch. Stoch. Reports 57 1996 159-167
25. Z.-M. Ma M. Röckner Introduction to the Theory of (non-symmetric) Dirichlet Forms 1992 Springer Berlin
26. U. Mosco Composite media and Dirichlet forms J. Funct. Anal. 123 1994 368-421
27. B. Muckenhoupt Weighted norm inequalities for Hardy maximal functions Trans. Amer. Math. Soc. 165 1972 207-226
28. Y. Ogura M. Tomisaki M. Tsuchiya Convergence of local type Dirichlet forms to a non-local type one Ann. Inst. H. Poincaré-PR 38 4 2002 507-556
29. A. Posilicano Convergence of distortet Brownian motions and singular Hamiltonians Potential Analysis 5 1996 241-271
30. C. Preston Random fields Lecture Notes in Mathematics vol. 534 1976 Springer Berlin, New York
31. O. Pugachev On closability of classical Dirichlet forms J. Funct. Anal. 207 2 2004 330-343
32. M. Röckner B. Schmuland Tightness of general C 1, p -capacities on Banach space J. Funct. Anal. 108 1992 1-12
33. M. Röckner T.S. Zhang Uniqueness of generalized Schrödinger operators and applications J. Funct. Anal. 105 1992 187-231
34. M. Röckner T.S. Zhang Uniqueness of generalized Schrödinger operators and applications II J. Funct. Anal. 119 1994 455-467
35. M. Röckner T.S. Zhang Finite dimensional approximations of diffusion processes on infinite dimensional state spaces Stoch. Stoch. Reports 57 1996 37-55
36. M. Röckner T.S. Zhang Convergence of operators semigroups generated by elliptic operators Osaka J. Math. 34 1997 923-932
37. p -Liouville properties J. Reine Angew. Math. 456 1994 173-196
38. K.T. Sturm Analysis on local Dirichlet spaces II. Upper Gaussian estimates for the fundamental solution of parabolic equations Osaka J. Math. 32 1995 275-312
39. M. Takeda On a martingal method for symmetric diffusion processes and its applications Osaka J. Math. 26 1989 605-623
40. T. Uemura On weak convergence of diffusion processes generated by energy forms Osaka J. Math. 32 1995 861-868
41. V.V. Zhikov Weighted Sobolev spaces Sbornik: Mathematics 189 8 1998 1139