[图书][B] Probabilistic theory of mean field games with applications I-II
The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …
games with a common noise. We develop a general two-step strategy for the search of weak …
[HTML][HTML] Mean field analysis of neural networks: A central limit theorem
J Sirignano, K Spiliopoulos - Stochastic Processes and their Applications, 2020 - Elsevier
We rigorously prove a central limit theorem for neural network models with a single hidden
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …
[图书][B] Effective dynamics of stochastic partial differential equations
J Duan, W Wang - 2014 - books.google.com
Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …
differential equations with slow and fast time scales, or large and small spatial scales. The …
[图书][B] An introduction to stochastic filtering theory
J Xiong - 2008 - books.google.com
Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic
processes that arise in many applied fields including communication, target-tracking, and …
processes that arise in many applied fields including communication, target-tracking, and …
From the master equation to mean field game limit theory: a central limit theorem
Mean field games (MFGs) describe the limit, as n tends to infinity, of stochastic differential
games with n players interacting with one another through their common empirical …
games with n players interacting with one another through their common empirical …
Finite state mean field games with Wright–Fisher common noise
We force uniqueness in finite state mean field games by adding a Wright–Fisher common
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …
Analysis of a finite state many player game using its master equation
E Bayraktar, A Cohen - SIAM Journal on Control and Optimization, 2018 - SIAM
We consider an n-player symmetric stochastic game with weak interactions between the
players. Time is continuous, and the horizon and the number of states are finite. We show …
players. Time is continuous, and the horizon and the number of states are finite. We show …
[图书][B] Stochastic ordinary and stochastic partial differential equations
P Kotelenez - 2008 - Springer
The present volume analyzes mathematical models of time-dependent physical phenomena
on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous …
on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous …
[HTML][HTML] Gaussian fluctuations for interacting particle systems with singular kernels
We consider the asymptotic behaviour of the fluctuations for the empirical measures of
interacting particle systems with singular kernels. We prove that the sequence of fluctuation …
interacting particle systems with singular kernels. We prove that the sequence of fluctuation …
[HTML][HTML] Weakly interacting particle systems on inhomogeneous random graphs
We consider weakly interacting diffusions on time varying random graphs. The system
consists of a large number of nodes in which the state of each node is governed by a …
consists of a large number of nodes in which the state of each node is governed by a …