Existence of solutions to path-dependent kinetic equations and related forward - backward systems

TL;DR

This paper investigates path-dependent kinetic equations related to mean field games, establishing local and global solutions along with regularity properties, thus advancing the mathematical understanding of these complex systems.

Contribution

It provides new existence, uniqueness, and regularity results for path-dependent kinetic equations linked to forward-backward mean field game systems.

Findings

Established local well-posedness of the equations

Proved global existence of solutions

Analyzed regularity properties of solutions

Abstract

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.