Weak Convergence for the Fourth-Order Stochastic Heat Equation with Fractional Noises

In this paper, we study a fourth-order stochastic heat equation with homogeneous Neumann boundary conditions and double-parameter fractional noises. We formally replace the random perturbation by a family of noisy inputs depending on a parameter n is an element of N which approximates the noises. Then we provided sufficient conditions ensuring that the real-valued mild solution of the fourth-order stochastic heat equation driven by this family of noises converges in law, in the space of C([0, T] x [0, pi]) of continuous functions, to the solution of a class of fourth-order stochastic heat equation driven by fractional noises.