2018/01/26 by Simone Cacace, Fabio Camilli, Cacace, Simone +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP
paper · pdf · doi:10.48550/arxiv.1801.08828
arxiv created 2018/01/26 · openalex publication_date 2018/01/26 · arxiv updated 2018/01/29 · openalex created_date 2018/02/02 · openalex updated_date 2026/07/28
This paper is devoted to some qualitative descriptions and some numerical results for ergodic Mean Field Games systems which arise, e.g., in the homogenization with a small noise limit. We shall consider either power type potentials or logarithmic type ones. In both cases, we shall establish some qualitative properties of the effective Hamiltonian H and of the effective drift b. In particular we shall provide two cases where the effective system keeps/looses the Mean Field Games structure, namely where ∇P H(P,α) coincides or not with b(P, α). On the other hand, we shall provide some numerical tests validating the aforementioned qualitative properties of H and b. In particular, we provide a numerical estimate of the discrepancy ∇P H(P,α)- b(P, α).