Generalized Mehler semigroups and applications

Probability Theory and Related Fields

Volumn 105, Issue 2, 1996, Pages 193-225

  Bogachev, Vladimir I ^a   Röckner, Michael ^b   Schmuland, Byron ^c  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b BIELEFELD UNIVERSITY   (Germany)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040517192     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01203835     Document Type: Article

References (32)

1. Albeverio, S., Ma, Z.M., Röckner, M.: Local property of Dirichlet forms and diffusions on general state spaces. Math. Ann. 296, 677-686 (1993)
2. Albeverio, S., Röckner, M.: Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Probab. Theory Relat. Fields 89, 347-386 (1991)
3. Albeverio, S., Röckner, M.: Dirichlet form methods for uniqueness of martingale problems and applications. In: Cranston, M., Pinsky, M.: Stochastic analysis (Proceedings of Symposia in Pure Mathematics, vol. 57, pp. 513-528) Providence, Rhode Island: American Math. Society 1995
4. Bauer, H.: Wahrscheinlichkeitstheorie. Berlin New York: de Gruyter 1991
5. Berg, C., Forst, G.: Potential theory on locally compact abelian groups. Berlin Heidelberg New York: Springer 1975
6. Bogachev, V., Lescot, P., Röckner, M.: Pseudo-differential operators on infinite-dimensional spaces and martingale problems. Preprint 1995
7. Bogachev, V., Röckner, M.: Les capacités gaussiennes sont portées par des compacts métrisables. C.R. Acad. Sci. Paris 315, 197-202 (1992)
8. Bogachev, V.I., Röckner, M.: Mehler formula and capacities for infinite dimensional Ornstein-Uhlenbeck processes with general linear drift. Osaka J. Math. 32, 237-274 (1995)
9. Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Cambridge: Cambridge University Press 1992
10. Dynkin, E.B.: Die Grundlagen der Theorie der Markoffschen Prozesse. Berlin Heidelberg New York: Springer 1971
11. Fernique, X.: Intégrabilité des vecteurs gaussiens. C.R. Acad. Sci. Paris 270, 1698-1699 (1970)
12. Fernique, X.: Régularité des trajectoires des fonctions aléatoires gaussiennes. In: Dold, A., Eckmann, B.: Ecole d'Eté de Probabilités de Saint-Flour IV (Lect. Notes Math., vol. 480, pp. 1-96) Berlin Heidelberg New York: Springer 1975
13. Feyel, D., De La Pradelle, A.: Opérateurs linéaires et espaces de Sobolev sur l'espace de Wiener. C.R. Acad. Sci. Paris 313, 727-729 (1991)
14. Feyel, D., De La Pradelle, A.: Opérateurs linéaires gaussiens. Potential Anal. 3, 89-105 (1994)
15. Feyel, D., De La Pradelle, A.: Brownian processes in infinite dimensions. Potential Anal. 4, 173-183 (1995)
16. Fuhrman, M.: Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces. Preprint 1993
17. Fuhrman, M., Röckner, M.: Recent results on generalized Mehler semigroups. In preparation
18. Fukushima, M.: Dirichlet forms and Markov processes. Amsterdam: North-Holland 1980
19. Ma, Z.M., Röckner, M.: Introduction to the theory of (non-symmetric) Dirichlet forms. Berlin Heidelberg New York: Springer 1992
20. Millet, A., Smoleński, W.: On the continuity of Ornstein-Uhlenbeck processes in infinite dimensions. Probab. Theory Relat. Fields 92, 529-547 (1992)
21. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Berlin Heidelberg New York: Springer 1983
22. Reed, M., Simon, B.: Methods of modern mathematical physics II: Fourier analysis, self-adjointness. San Diego: Academic Press 1975
23. Röckner, M.: Traces of harmonic functions and a new path space for the free quantum field. J. Funct. Anal. 79, 211-249 (1988)
24. Röckner, M.: On the transition function of the infinite dimensional Ornstein-Uhlenbeck process given by the free quantum field. In: Kral, J. et al.: Potential theory. New York London: Plenum Press 1988
25. Röckner, M.: On the parabolic Martin boundary of the Ornstein-Uhlenbeck operator on Wiener space. Ann. Probab. 20, 1063-1085 (1992)
26. Röckner, M., Schmuland, B.: Quasi-regular Dirichlet forms: examples and counterexamples. Canad. J. Math. 47, 165-200 (1995)
27. Rozovskii, B.L.: Stochastic evolution systems. Dordrecht: Kluwer Acad. Publ. 1990 (Russian edition: Moscow: Nauka 1983)
28. Schmuland, B.: Dirichlet forms with polynomial domain. Mathematica Japonica 37, 1015-1024 (1992)
29. Schmuland, B.: Non-symmetric Ornstein-Uhlenbeck processes in Banach space via Dirichlet forms. Canad. J. Math. 45, 1324-1338 (1993)
30. Schmuland, B.: On the local property for positivity preserving coercive forms. In: Ma, Z.M. et al.: Dirichlet forms and stochastic processes, Proc. International Conference held in Beijing, China, October 25-31, 1993, pp. 345-354. Berlin New York: de Gruyter 1995
31. Vakhania, N.N., Tarieladze, V.I., Chobanyan, S.A.: Probability distributions on Banach spaces. Dordrecht: Reidel 1987
32. Zakai, M., Snyders, J.: Stationary probability measures for linear differential equations driven by white noise. J. Diff. Equations 8, 27-33 (1970)