The ergodic Mean Field Game system for a type of state constraint condition
Analysis of PDEs
2021-07-27 v2
Abstract
This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this setting, the infinite boundary condition prevents the underlying stochastic trajectories from reaching the boundary, resulting in a state constraint solution. We consider a class of superlinear power-like Hamiltonians and establish existence and uniqueness results under appropriate assumptions on the coupling. We treat both non-local and local couplings, and establish the uniqueness of the system by exploiting the decay of the density near the boundary.
Keywords
Cite
@article{arxiv.2101.10564,
title = {The ergodic Mean Field Game system for a type of state constraint condition},
author = {Mariya Sardarli},
journal= {arXiv preprint arXiv:2101.10564},
year = {2021}
}