AI 中文总结
本文通过测度空间上的PDE技术，为带消失噪声的平均场粒子系统建立大偏差原理，证明传递函数收敛至Hamilton-Jacobi方程粘性解，并借最优控制显式导出率函数。
AI 中文摘要
本文提出了一种稳健的策略，用于建立T d中具有消失噪声的平均场相互作用粒子系统的大偏差原理。将此视为Freidlin-Wentzell型问题，我们的方法依赖于概率测度空间上偏微分方程（简称PDE）的近期技术[5]。我们首先以自包含的方式概述了PDE方法处理大偏差的证明策略。随着粒子数趋于无穷，我们随后证明系统的传递函数收敛到概率测度空间上极限Hamilton-Jacobi方程的唯一粘性解。最后，通过将该极限PDE的解表述为最优控制问题的值函数，我们显式地推导出率函数。
英文摘要
This paper introduces a robust strategy to establish large deviation principles for mean field interacting particle systems in T d with vanishing noise. Viewed as a Freidlin-Wentzell type problem, our approach relies on recent techniques for partial differential equations (in short PDE) on the space of probability measures [5]. We first outline the proof strategy for the PDE approach to large deviations in a self-contained manner. As the number of particles goes to infinity, we then show that the transfer function of the system converges to the unique viscosity solution of a limiting Hamilton-Jacobi equation on the space of probability measures. Finally, we explicitly derive the rate function by formulating the solution of this limiting PDE as the value function of an optimal control problem.
