This paper examines the stochastic averaging principle of fast-slow-coupled neutral stochastic differential equations with time-varying delay. Due to the presence of neutral terms, traditional martingale methods and weak convergence techniques are not directly applicable. To overcome these difficulties, this paper gives a more subtle proof for tightness of the slow-varying process. To characterize the limit neutral diffusion system, more complicated computations and more subtle techniques are needed to deal with the neutral term. As a byproduct, this paper also establishes the equivalence between the weak solution of the neutral stochastic differential equation with time-varying delay and the solution of its corresponding the martingale problem.

本文研究了时变时滞快慢耦合中性随机微分方程的随机平均原理。由于中性项的存在，传统的鞅方法和弱收敛技术不能直接适用。为了克服这些困难，本文对慢变过程的紧密性给出了更微妙的证明。为了表征极限中性扩散系统，需要更复杂的计算和更微妙的技术来处理中性项。作为副产品，本文还建立了时变时滞中性随机微分方程的弱解与其对应的鞅问题的解之间的等价性。