Support Theorem for Stochastic Differential Equations with Sobolev Coefficients
- 71 Downloads
In this paper we prove a support theorem for stochastic differential equations with Sobolev coefficients in the framework of DiPerna-Lions theory.
KeywordsSupport theorem Stochastic differential equation DiPerna-Lions theory
Mathematics Subject Classification (2010)60H10 60F15
Unable to display preview. Download preview PDF.
The first author is very grateful to Professor Xicheng Zhang for his encouragement and useful discussions. The authors would also like to thank the anonymous referees and the editor for their careful reading of manuscript, correcting errors and making very helping suggestions, which improve the quality of this paper. This work was supported by China NSF Grant No.U1504620, 11471104, and Youth Science Foundation of Henan Normal University Grant No.2014QK02.
- 5.Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. Czechoslovak North-Holland, Amsterdam, Kodansha, Tokyo (1981)Google Scholar
- 8.Millet, A., Sanz-Solé, M.: A simple proof of the support theorem for diffusion processes. In: Séminaire de Probabilités, XXVIII, Lecture Notes in Math, p 1583. Springer, Berlin (1994)Google Scholar
- 13.Triebel, H.: Interpolation theory, function spaces, differential operators. North–Holland, Amsterdam (1978)Google Scholar