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Session Overview |
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S 3 Keynote: Stochastic Analysis and S(P)DEs
Session Topics: 3. Stochastic Analysis and S(P)DEs
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2:50 pm - 3:40 pm
Mean field control with infinite dimensional common noise Mean field control and its twin theory of mean field games have undergone many developments since the early works of Lasry and Lions, and Huang, Caines, and Malhamé. In a nutshell, both theories aim at the asymptotic analysis of equilibria within large populations of rational agents in weak interaction. In the case of control, the equilibria are asymptotically understood as solutions to an optimization problem posed on a McKean-Vlasov type dynamics. From an Eulerian point of view, the value function is the solution of a Hamilton-Jacobi equation on the space of probability measures. The underlying objective of this presentation is to construct stochastic versions of this problem in which the measure-valued dynamics is itself random, and in particular subject to a noise that is sufficiently regularizing to smooth the Hamilton-Jacobi equation. In this presentation, we give two examples of such noise. Based on joint works with W. Hammersley, M. Martini and G. Sodini | ||
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