# Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems

@inproceedings{Koloklotsov2013ExistenceOS, title={Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems}, author={Vassili Koloklotsov and Wei Yang}, year={2013} }

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.

## 16 Citations

Sensitivity analysis for HJB equations with an application to a coupled backward-forward system

- Mathematics
- 2013

In this paper, we analyse the dependence of the solution of Hamilton-Jacobi-Bellman equations on a functional parameter. This sensitivity analysis not only has the interest on its own, but also is…

Abstract McKean–Vlasov and Hamilton–Jacobi–Bellman Equations, Their Fractional Versions and Related Forward–Backward Systems on Riemannian Manifolds

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In this paper, we study mean ﬁeld games with mean-ﬁeld-dependent volatility, and associated fully coupled nonlocal quasilinear forward-backward PDEs (FBPDEs). We show the global intime existence of…

On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players

- MathematicsDyn. Games Appl.
- 2014

It is shown that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean filed game model represent a 1/N-Nash equilibrium for approximating systems of N agents.

A 1/n Nash equilibrium for non-linear Markov games of mean-field-type on finite state space

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- 2014

We investigate mean field games for players, who are weakly coupled via their empirical measure. To this end we investigate time-dependent pure jump type propagators over a finite space in the…

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- 2014

We investigate mean field games from the point of view of a large number of indistinguishable players which eventually converges to in- finity. The players are weakly coupled via their empirical…

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- MathematicsAutom. Remote. Control.
- 2016

The main result of the paper is that any solution of the limiting mean field consistency equation generates a 1/N-Nash equilibrium for the approximating game of N agents.

On mean field games with common noise and McKean-Vlasov SPDEs

- MathematicsStochastic Analysis and Applications
- 2019

Abstract We formulate the MFG limit for N interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We…

Dynamic Programming for Mean-Field Type Control

- MathematicsJ. Optim. Theory Appl.
- 2016

A Hamilton–Jacobi–Bellman fixed-point algorithm is compared to a steepest descent method issued from calculus of variations and an extended Bellman’s principle is derived by a different argument.

An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space

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- 2016

We investigate mean-field games from the point of view of a large number of indistinguishable players, which eventually converges to infinity. The players are weakly coupled via their empirical…

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