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In this paper, we study the central limit theorem for a perturbed stochastic heat equation in the whole space $\mathbb{R}^{d}$, $d\ge 1$. This equation is driven by a Gaussian noise, which is white in time and correlated in space, and the differential operator is a fractional derivative operator. Burkholder’s inequality plays an important role in the proof.

Central limit theorem for a fractional stochastic heat equation with spatially correlated noise