Abstract
In this paper, we discuss a stochastic analogue ofAubry-Mather theory in which a deterministic control problemis replaced by a controlled diffusion. We prove theexistence of a minimizing measure (Mather measure) and discussits main properties using viscosity solutionsof Hamilton-Jacobi equations. Then we prove regularity estimateson viscosity solutions of the Hamilton-Jacobi equationusing the Mather measure. Finally, we apply these results toprove asymptotic estimates on the trajectories of controlled diffusions andstudy the convergence of Mather measures as the rate of diffusion vanishes.
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.
