Special Session 19: Stochastic Partial Differential Equations

Mean field game systems with common noise and degenerate idiosyncratic noise

Benjamin D Seeger
University of Texas at Austin
Co-Author(s):    P. Cardaliaguet, P. Souganidis
I will describe the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. A new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations must be developed, and this is used to build probabilistically weak solutions of the mean field game system. The uniqueness of a strong solution can be proved under additional structural assumptions.