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

  title={Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems},
  author={Vassili Koloklotsov and Wei Yang},
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. 
Sensitivity analysis for HJB equations with an application to a coupled backward-forward system
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
We introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the Mc-Kean-Vlasov-type equations describing nonlinear Markov processes and the
Mean Field Games with Mean-Field-Dependent Volatility, and Associated Fully Coupled Nonlocal Quasilinear Forward-Backward Parabolic Equations
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
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
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
An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces
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
Mean field games based on stable-like processes
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
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
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
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


Nonlinear Markov Processes and Kinetic Equations
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
Stochastic partial dierential equations whose solutions are probability-measurevalued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of innite
Nash Equilibria for Large-Population Linear Stochastic Systems of Weakly Coupled Agents
We consider dynamic games in large population conditions where the agents evolve according to non-uniform dynamics and are weakly coupled via their dynamics and the individual costs. A state
Nonlinear Diffusions and Stable-Like Processes with Coefficients Depending on the Median or VaR
The paper is devoted to the well-posedness for nonlinear McKean-Vlasov type diffusions with coefficients depending on the median or, more generally, on the α-quantile of the underlying distribution.
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent at the microscopic level and the mass of individuals at the macroscopic level.
Markov Processes, Semigroups and Generators
Part I Brownian Motion, Markov Processes, Martingales. 1 Preliminaries in Probability and Analysis. 2 Browninan Motion I: Constructions. 3 Martingales and Markov Processes. 4 Browninan Motion II:
The NCE (Mean Field) Principle With Locality Dependent Cost Interactions
This work studies large population stochastic dynamic games where each agent assigns individually determined coupling strengths to the states of other agents in its performance function and generates an -Nash equilibrium for the population of size.
Foundations of Modern Probability
  • O. Kallenberg
  • Mathematics
    Probability Theory and Stochastic Modelling
  • 2021
* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit
Mean Field Games and Applications
This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-Michel Lasry. This course was based upon the articles of the three authors and upon unpublished materials they
Nonlinear Mark tions. Cambridge Track 182
  • Cambridge University Press, Cambridge, 2010.
  • 2010