Strong convergence rate in averaging principle for stochastic   hyperbolic-parabolic equations with two time-scales
  In this article, we investigate averaging principle for stochastic hyperbolic-parabolic equations with two time-scales, in which both the slow and fast components are perturbed by multiplicative noises. Particularly, we prove that the rate of strong convergence for the slow component to the averaged dynamics is of order $1/2$, which significantly improves the order $1/4$ established in our previous work. 
Hongbo Fu, Li Wan, Jicheng Liu, Xianming Liu
math.PR