Abstract
After fundamental works of K. Ito in 1940s, theory of stochastic differential equations (SDE) has been studied extensively. The flow property of the solution of SDE was studied around 1980 by Elworthy, Bismut, Ikeda-Watanabe, Kunita, Meyer etc. It was proved that under the Lipschitz condition of the coefficients of the equation, the solution of any SDE driven by a Brownian motion or a continuous semimartingale admits a version of a stochasic flows of homeomorphisms. Further if the coefficients are smooth, it admits a version of a stochastic flow of diffeomorphisms. Details are found in Kunita’s book [11]. In this paper, we will be mainly concerned with SDE driven by a Levy process or a semimartingale with jumps and discuss the flow property of the solutions. Before we introduce our SDE, let us briefly recall the relation between SDE driven by a Brownian motion or a continuous semimartingle and a stochastic flow of homeomorphisms.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
