Digital search trees and chaos game representation

均场 Langevin 动力学、控制与博弈中的尖锐混沌传播

Sharp propagation of chaos for mean field Langevin dynamics, control, and games

本文研究了均场 Langevin 动力学、控制与博弈中混沌传播的尖锐速率，结合 BBGKY 层次结构与弱混沌传播技术，推导了有限时间和均匀时间下的收敛速率结果。

On the convergence rate of the chaos game

This paper studies how long it takes the orbit of the chaos game to reach a certain density inside the attractor of a strictly contracting iterated function system of which we only assume that its lower dimension is positive. We show that the rate of growth of this cover time is determined by the Minkowski dimension of the push-forward of the shift invariant measure with exponential decay of correlations driving the chaos game. Moreover, we bound the expected value of the cover time from above and below with multiplicative logarithmic correction terms. As an application, for Bedford-McMullen c…

Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactions

In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with respect to the interacting graphons which are necessary to show propagation of chaos results. As an application of propagation of chaos, we prove the convergence of n-player game Nash equilibrium for a general model, which is new in the theory of graphon mean field games.

Convergence of large population games to mean field games with interaction through the controls

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by stochastic analysis methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds f…

具有受控波动率的位移单调平均场博弈的定量收敛

Quantitative convergence for displacement monotone mean field games with controlled volatility

研究具有共同噪声和受控波动率的平均场博弈收敛问题，通过最大值原理将其转化为前向-后向混沌传播问题，并利用位移单调性首次为共同噪声受控博弈提供了开环Nash均衡的定量收敛证明。