An averaging principle for fast-slow-coupled neutral stochastic differential equations with time-varying delay. (English) Zbl 1523.60107
Summary: 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34K40 | Neutral functional-differential equations |
| 34K26 | Singular perturbations of functional-differential equations |
Keywords:
averaging principle; two-time scales; neutral stochastic differential equations; time-varying delay; martingale problemReferences:
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