Abstract
The boundaries of a semi-simple Lie group G in this paper are slightly more general than Furstenberg's boundaries. The horizontal diffusion gt in G induces a stochastic flow on any boundary of G, whose one point motion is a Brownian motion. The global and local stability of the flow are established, using the limiting property of gt under the Iwasawa decomposition. The Lyapunov spectrum contains only negative exponents and the associated filtration are determined by the root space structure of G. In this way, we obtain many interesting examples of Lie group-valued stochastic flows on compact spaces, including the gradient flow and other finite dimensional flows on spheres
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.
