  We study the asymptotic behavior of stochastic hyperbolic parabolic equations
with slow and fast time scales. Both the strong and weak convergence in the
averaging principe are established, which can be viewed as a functional law of
large numbers. Then we study the stochastic fluctuations of the original system
around its averaged equation. We show that the normalized difference converges
weakly to the solution of a linear stochastic wave equation, which is a form of
functional central limit theorem. We provide a unified proof for the above
convergence by using the Poisson equation in Hilbert spaces. Moreover, sharp
rates of convergence are obtained, which are shown not to depend on the
regularity of the coefficients in the equation for the fast variable.
