Probabilistic representations and hyperbound estimates for semigroups

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 2, Issue 3, 1999, Pages 337-358

  Rockner M ^a   Zhang, T S ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b WESTERN NORWAY UNIVERSITY OF APPLIED SCIENCES   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0348098647     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025799000205     Document Type: Article

References (20)

1. S. Albeverio, Y. G. Kondratiev and M. Röckner, Dirichlet operators via stochastic analysis J. Funct. Anal. 128 (1995) 102-138.
2. S. Albeverio and M. Röckner, Stochastic differential equations in infinite-dimensions: Solutions via Dirichlet forms, Probab. Theory Related Fields 89 (1991) 347-386.
3. S. Albeverio, M. Röckner and T. S. Zhang, Girsanov transform for symmetric diffusions with infinite dimensional state space, Ann. Probab. 21 (1993) 961-978.
4. S. Aida and I. Shigekawa, Logarithmic Sobolev inequalities and special gaps: Perturbation Theory, J. Funct. Anal. 127 (1994) 448-475.
5. V. Bogachev, M. Röckner and T. S. Zhang, Existence of invariant measures: A quadratic form approach, preprint, Bielefeld, 1997.
6. M. Fukushima, Dirichlet Forms and Markov Processes (North-Holland, 1980).
7. J. Glover, M. Rao, H. Sikic and R. Song, Quadratic forms corresponding to the generalized Schödinger semigroups, J. Funct. Anal. 125 (1994) 358-379.
8. L. Gross, Logarithmic Sobolev inequalities and contractive properties of semigroups, in Dirichlet Forms, eds. G. Dellntonio and U. Mosco (Springer-Verlag, 1993).
9. M. Hino, Existence of invariant measures for diffusion processes on a Wiener space, preprint 1997.
10. N. Ikeda and S. Watanable, Stochastic Differential Equations and Diffusion Processes (North-Holland and Kodansha, 1981).
11. T. J. Lyons and T. S. Zhang, Decomposition of Dirichlet processes and its applications, Ann. Probab. 22 (1994) 494-524.
12. T. J. Lyons and T. S. Zhang, Convergence of non-symmetric Dirichlet processes, Stochastics and Stochastics Rep. 57 (1996) 159-167.
13. T. J. Lyons, J. Lunt and T. S. Zhang, Integrability of functional of Dirichlet processes, Probabilistic representations of semigroups and estimates of heat kernels, J. Funct. Anal. 153 (1998) 320-342.
14. T. J. Lyons and W. A. Zheng, Acrossing estimate for the canonical process on a Dirichlet space and tightness result, Colloque Paul Levy sur les processes stochastoque, Asterisque (1988) 157-158, 248-272.
15. Z. M. Ma and M. Röckner, Introduction to the Theory of (NonSymmetric) Dirichlet Forms (Springer-Verlag, 1992).
16. M. Röckner and T. S. Zhang, Uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal. 105 (1992) 187-231.
17. M. Röckner and T. S. Zhang, Convergence of operators semigroups generated by elliptic operators, Osaka J. Math. 34 (1997) 923-932.
18. B. Simon and R. Høegh-Krohn, Hypercontractive semigroups and two-dimensional self-coupled Bose fields, J. Funct. Anal. 9 (1972) 121-180.
19. W. Stannat, The theory of generalized Dirichlet forms and its applications in analysis and stochastics, Ph.D. thesis, Bielefeld, 1997.
20. T. S. Zhang, Generalized Feynman-Kac semigroups, associated quadratic forms and asymptotic properties, Preprint 1998, to appear in Potential Anal.