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A generalization of the Hopf-Cole transformation for stationary Mean Field Games systems By Dr. Marco Cirant (Università di Milano, Italy)

  • Class schedule:  Monday, Feb. 25th, 2015   from  03:00 pm to 04:00 pm
  • Location: Building 1, Room 4214
  • Refreshments:  Available @ 02:45 pm ​​

Abstract
 
Mean Field Games systems aim at modeling and analyzing decision processes involving a very large number of indistinguishable rational agents. A stationary MFG system consists of an Hamilton-Jacobi-Bellman equation coupled with a Kolmogorov equation. In the particular case of quadratic dependance of the Hamiltonian with respect to the velocity, this elliptic system can be turned into a single semilinear equation by means of the so-called Hopf-Cole transformation. In the present talk we discuss a generalization of this transformation that applies to some MFG systems with non-quadratic Hamiltonian. In particular, under suitable assumptions, it is possible to rewrite the HJB equation as a quasi-linear elliptic equation involving the r-Laplacian. We show an application of this transformation to uniqueness problems for MFG systems with aggregation.

Biography
 
Marco Cirant is a post-doctoral fellow at Dipartimento di Matematica, Università di Milano. Dr. Cirant received his M.Sc. (2010) in Mathematics from Università di Milano. In 2014, Dr. Cirant obtained his Ph.D. in Mathematics from Università di Padova, under the supervision of Prof. Martino Bardi. His research areas are viscosity methods for non-linear Partial Differential Equations, Mean Field Games and stochastic ergodic control.