Kolmogorov equations for measures

Journal of Evolution Equations

Volumn 8, Issue 2, 2008, Pages 231-262

  Manca, Luigi ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Kolmogorov operators; Markov semigroups; Measure valued equations

Indexed keywords

EID: 44549085663     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-008-0335-1     Document Type: Article

References (24)

1. BOGACHEV, V. I. DA PRATO, G. and RÖCKNER, M., Existence of solutions to weak parabolic equations for measures, Proc. London Math. Soc. 88(3) (2004), 753-774.
2. BOGACHEV, V. I. and RÖCKNER, M., A generalization of Khasminskii's theorem on the existence of invariant measures for locally integrable drifts, Teor. Veroyatnost. i Primenen. 45(3) (2000), 417-436.
3. _, Elliptic equations for measures on infinite-dimensional spaces and applications, Probab. Theory Related Fields, 120(4) (2001), 445-496,
4. CERRAI, S., A Hille-Yosida theorem for weakly continuous semigroups, Semigroup Forum 49(3) (1994), 349-367,
5. DA PRATO, G., Kolmogorov equations for stochastic PDEs, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser Verlag, 2004.
6. DA PRATO, G. and TUBARO, L., Some results about dissipativity of Kolmogorov operators, Czechoslovak Math. J. 51 (126)(4) (2001), 685-699.
7. DA PRATO, G. and ZABCZYK, J., Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, 1992.
8. DA PRATO, GIUSEPPE and ZABCZYK, JERZY., Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, vol. 229, Cambridge University Press, 1996.
9. _, Second order partial differential equations in Hilbert spaces, London Mathematical Society Lecture Note Series, vol. 293, Cambridge University Press, 2002.
10. ENGEL, KLAUS-JOCHEN and NAGEL, RAINER., One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000.
11. ETHIER, S. N. and KURTZ, T. G., Markov processes, characterization and convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., 1986.
12. b(H), Semigroup Forum 68(1) (2004), 87-107.
13. GOLDYS, B. and KOCAN, M., Diffusion semigroups in spaces of continuous functions with mixed topology, J. Differential Equations 173(1) (2001), 17-39.
14. HASMINSKII, R. Z., Stochastic stability of differential equations, Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, vol. 7, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980, Translated from the Russian by D. Louvish.
15. KÖRNER, T. W., Fourier analysis, 2 ed., Cambridge University Press, 1989.
16. KÜHNEMUND, F., Bi-Continuous Semigroups on Spaces with Two Topologies: Theory and Applications, Ph. D. thesis, Universität Tübingen, 2001.
17. _, A Hille-Yosida theorem for bi-continuous semigroups, Semigroup Forum 67(2) (2003), 205-225.
18. LANT, T. and THIEME, H. R., Markov transition functions and semigroups of measures, Semigroup Forum 74(3) (2007), 337-369.
19. LASRY, J.-M. and LIONS, P.-L., A remark on regularization in Hilbert spaces, Israel J. Math. 55(3) (1986), 257-266.
20. n, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(1) (1997), 133-164.
21. MANCA, L., On a class of stochastic semilinear PDEs, Stoch. Anal. Appl. 24(2) (2006), 399-426.
22. PRIOLA, E., On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Math. 136(3) (1999), 271-295.
23. SCHMEIDLER, W., Linear operators in Hilbert space, Translation by Jay Strum. Revised and edited by A. Shenitzer and D. Sol itar, Academic Press, New York, 1965,
24. YOSIDA, K., Functional analysis, Classics in Mathematics, Springer-Verlag, 1995, Reprint of the sixth (1980) edition.