Finite state Mean Field Games with Wright-Fisher common noise
Résumé
We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on the simplex whose characteristics solve the stochastic forward-backward system associated with the mean field game; see Cardaliaguet et al. [10]. We show that this equation, which is a non-linear version of the Kimura type equation studied in Epstein and Mazzeo [28], has a unique smooth solution whenever the normal component of the drift at the boundary is strong enough. Among others, this requires a priori estimates of Holder type for the corresponding Kimura operator when the drift therein is merely continuous.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)