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C3 Guest Lecture Series

Time Asymptotics of a Class of Mean-Field Equations
Ari Arapostathis
Ari Arapostathis is currently with the University of Texas at Austin, where he is a Professor in the Department of Electrical and Computer Engineering. He received his B.S. from MIT and his Ph.D. from U.C. Berkeley. His research interests include stochastic control theory, control applications to networks, and hybrid systems. Among his main technical contributions are in the areas of adaptive control and estimation of stochastic systems with partial observations, stochastic hybrid systems, adaptive control of nonlinear systems, geometric nonlinear theory, and stability of large scale interconnected power systems. A Fellow of IEEE, and a member of AMS and SIAM, he was a past Associate Editor of the IEEE Transactions on Automatic Control and the Journal of Mathematical Systems and Control. His research has been supported by several grants from the National Science Foundation, the Air-Force Office of Scientific Research, DARPA, the Office of Naval Research, the Texas Advanced Research/Technology Program and industry.
In this talk, we shall examine the time-asymptotic behavior of a class of McKean-Vlasov Hamilton-Jacobi-Bellman (HJB) equations arising in mean-field games of the Lasry-Lions type, but for a more general diffusion matrix, drift vector and running cost. We are going to review how these equations arise and then show that the law of the process associated with the solution of the HJB converges asymptotically in time to the law of the stationary solution and so does the value function. The analysis relies in part on our recent work on the convergence of the relative value iteration for controlled diffusions. This employs concepts and results from the general theory of monotone dynamical systems, which we will independently review.
Friday, January 25, 2013
2:00 p.m.
234 Larsen

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