多类有限状态平均场系统的大时间行为
Large-time behavior of finite-state mean-field systems with multi-classes
摘要：
本文研究了一类多类有限状态平均场系统的经验向量的大时间渐近性。经验向量由表征系统内不同类别的本地经验度量组成。当系统中的粒子数趋于无穷大时，经验向量过程收敛到McKean-Vlasov系统的解。首先，我们研究了极限McKean-Vlasov系统不变分布的大偏差原理。然后，我们研究了在大尺度和大时间出现的亚稳态现象。最后，我们估计的收敛速率的经验向量过程的不变测度。在系统的局部齐性条件下，我们的结果建立在一个积空间中。
英文摘要：
We study in this paper the large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multi-classes. The empirical vector is composed of local empirical measures characterizing the different classes within the system. As the number of particles in the system goes to infinity, the empirical vector process converges towards the solution to a McKean-Vlasov system. First, we investigate the large deviations principles of the invariant distribution from the limiting McKean-Vlasov system. Then, we examine the metastable phenomena arising at a large scale and large time. Finally, we estimate the rate of convergence of the empirical vector process to its invariant measure. Given the local homogeneity in the system, our results are established in a product space.
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