An Averaging Principle for Fast–Slow-Coupled Neutral Stochastic Differential Equations with Time-Varying Delay.

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. [ABSTRACT FROM AUTHOR]