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Mountford","submitted_at":"2017-06-27T21:16:05Z","abstract_excerpt":"We consider the parabolic Anderson model driven by fractional noise: $$ \\frac{\\partial}{\\partial t}u(t,x)= \\kappa \\boldsymbol{\\Delta} u(t,x)+ u(t,x)\\frac{\\partial}{\\partial t}W(t,x) \\qquad x\\in\\mathbb{Z}^d\\;,\\; t\\geq 0\\,, $$ where $\\kappa>0$ is a diffusion constant, $\\boldsymbol{\\Delta}$ is the discrete Laplacian defined by $\\boldsymbol{\\Delta} f(x)= \\frac{1}{2d}\\sum_{|y-x|=1}\\bigl(f(y)-f(x)\\bigr)$, and $\\{W(t,x)\\;;\\;t\\geq0\\}_{x \\in \\mathbb{Z}^d}$ is a family of independent fractional Brownian motions with Hurst parameter $H\\in(0,1)$, indexed by $\\mathbb{Z}^d$. 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