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In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^k(t,x)\delta {\beta }_t^k,t\in [0,T]$, with random coefficients and , driven by a sequence () of i.i.d. fractional Brownian motions of index . Using the Malliavin calculus techniques and a -th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (), we prove that the equation has a unique solution (in a Banach space of summability exponent ≥ 2), and this solution is Hölder continuous in both time and space.

In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^k(t,x)\delta {\beta }_t^k,t\in [0,T]$, with random coefficients and , driven by a sequence () of i.i.d. fractional Brownian motions of index . Using the Malliavin calculus techniques and a -th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (), we prove that the equation has a unique solution (in a Banach space of summability exponent ≥ 2), and this solution is Hölder continuous in both time and space.