Averaging principle and normal deviations for multi-scale stochastic hyperbolic–parabolic equations

We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both strong and weak convergence in averaging principle are established. Then we fluctuations original system around its averaged equation. show that normalized difference converges weakly to solution a linear wave An extra diffusion term appears limit which is given explicitly terms Poisson Furthermore, sharp rates for above obtained, shown not depend on regularity coefficients equation fast variable.