An averaging principle for two-time-scale stochastic functional differential equations (Q1986531)

This paper is mainly concerned with functional diffusions with two-time scales in which the slow-varying process includes path-dependent functionals and the fast-varying process is a rapidly-changing diffusion. At first, mixed functional Itô formulas and the corresponding martingale representation are established, and an averaging principle via weak convergence methods is also developed. Finally, it is shown that the slow-varying process converges weakly to a stochastic functional differential equation whose coefficients are averages of that of the original slow-varying process w.r.t. the invariant measure of the fast-varying process.