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

Abstract

Abstract In this paper, we study the central limit theorem for a perturbed stochastic heat equation in the whole space R d $\mathbb{R}^{d}$ , d ≥ 1 $d\ge 1$ . 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.

Keywords

• Fractional derivative operator
• Stochastic heat equation
• Central limit theorem