On parabolic equations for measures

Communications in Partial Differential Equations

Volumn 33, Issue 3, 2008, Pages 397-418

  Bogachev, V I ^a   Da Prato, G ^b   Rockner M ^c,d  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b SCUOLA NORMALE SUPERIORE   (Italy)

^c BIELEFELD UNIVERSITY   (Germany)

^d PURDUE UNIVERSITY   (United States)

Author keywords

Existence; Parabolic equation for measures

Indexed keywords

EID: 40249108305     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300701382415     Document Type: Article

References (20)

1. Bogachev, V. I., Röckner, M. (1999). Elliptic equations for infinite dimensional probability distributions and Lyapunov functions. C. R. Acad. Sci. Paris, Sér. 1 329:705-710.
2. Bogachev, V. I., Röckner, M. (2000). A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts. Theory Probat. Appl. 45(3):417-436.
3. Bogachev, V. I., Röckner, M. (2001). Elliptic equations for measures on infinite-dimensional spaces and applications. Probab. Theory Related Fields 120(4):445-496.
4. Bogachev, V. I., Krylov, N. V., Röckner, M. (2001a). Differentiability of invariant measures and transition probabilities of singular diffusions. Dokl. Russian Acad. Sci. 376(2): 151-154.
5. Bogachev, V. I., Krylov, N. V., Röckner, M. (2001b). On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions. Comm. Partial Diff Equations 26(11-12):2037-2080.
6. Bogachev, V. I., Röckner, M., Wang, F.-Y. (2001c). Elliptic equations for invariant measures on finite and infinite dimensional manifolds. J. Math. Pures Appl. 80:177-221.
7. Bogachev, V.I., Röckner, M., Stannat, W. (2002). Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions. Sbornik Math. 193(7):945-976.
8. Bogachev, V. I., Da Prato, G., Röckner, M. (2004). Existence of solutions to weak parabolic equations for measures. Proc. London Math. Soc. (3) 88(3):753-774.
9. Bogachev, V. I., Röckner, M., Shaposhnikov, S. V. (2005). Global regularity and bounds for solutions of parabolic equations for probability measures. Theory Probab. Appl. 50(4): 652-674.
10. Bogachev, V. I., Da Prato, G., Röckner, M., Stannat, W. (2007a). Uniqueness of solutions to weak parabolic equations for measures. Bull. London Math. Soc. 39:631-640.
11. Bogachev, V. I., Röckner, M., Shaposhnikov, S. V. (2007b). Estimates of densities of stationary distributions and transition probabilities of diffusion processes. Theory Probab. Appl. 52(2):240-270.
12. Dohmann, J. (2005). Feller-type properties and path regularities of Markov processes. Forum Math. 17(3):343-360.
13. Gol'dshteǐn, V. M., Reshetnyak, Yu. G. (1990). Quasiconformal Mappings and Sobolev Spaces. Translated and revised from the 1983 Russian original. Dordrecht: Kluwer Academic Publ.
14. Krylov, N. V. (1999). An analytic approach to SPDEs. In: Carmona, R., Rozovskii, B., eds. Stochastic Partial Differential Equations: Six Perspectives. Rhode Island, Providence: Amer. Math. Soc., pp. 185-241.
15. Ladyz'enskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N. (1968). Linear and Quasilinear Equations of Parabolic Type. Rhode Island: Amer. Math. Soc.
16. Lieberman, G. M. (1996). Second Order Parabolic Differential Equations. Singapore: World Scientific.
17. 1: existence, uniqueness and associated Markov processes. Annali Scuola Normale Super, di Pisa Cl. Sci. (4) 28(1): 99-140.
18. 1. J. Evol. Equat. 4(4):463-495.
19. Stroock, D. W., Varadhan, S. R. S. (1979). Multidimensional Diffusion Processes. Berlin New York: Springer.
20. Wentzell, A. D. (1981). A Course in the Theory of Stochastic Processes. Translated from the Russian. New York: McGraw-Hill International Book.