Abstract
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 \(n\in {\mathbb {N}}\) 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 \(C([0,T]\times [0,\pi ])\) of continuous functions, to the solution of a class of fourth-order stochastic heat equation driven by fractional noises.
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