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As an application, we consider the fractional Laplacian equation with additive noises\n  \\bess du_t(x)=\\Delta^{\\frac{\\alpha}{2}}u_t(x)dt+\\sum_{k=1}^\\infty\\int_{\\mathbb{R}^m}g^k(t,x)z\\tilde N_k(dz,dt),\\ \\ \\ u_0=0,\\ 0\\leq t\\leq T,\n  \\eess where $\\Delta^{\\frac{\\alpha}{2}}=-(-\\Delta)^{\\frac{\\alpha}{2}}$, and $\\int_{\\mathbb{R}^m}z\\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump L\\'{e}vy processes with L\\'{e}vy measure of $\\nu^k$. 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