  We consider a 2D stochastic wave equation driven by a Gaussian noise, which
is temporally white and spatially colored described by the Riesz kernel. Our
first main result is the functional central limit theorem for the spatial
average of the solution. And we also establish a quantitative central limit
theorem for the marginal and the rate of convergence is described by the
total-variation distance. A fundamental ingredient in our proofs is the
pointwise $L^p$-estimate of Malliavin derivative, which is of independent
interest.

Probability