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### Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

ESAIM: Probability and Statistics

In this article, we consider the stochastic heat equation $du=\left(\Delta u+f\left(t,x\right)\right)\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^{k}\left(t,x\right)\delta {\beta }_{t}^{k},t\in \left[0,T\right]$, 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.

### -theory for the stochastic heat equation with infinite-dimensional fractional noise

ESAIM: Probability and Statistics

In this article, we consider the stochastic heat equation $du=\left(\Delta u+f\left(t,x\right)\right)\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^{k}\left(t,x\right)\delta {\beta }_{t}^{k},t\in \left[0,T\right]$, 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.

### A note on a Feynman-Kac-type formula.

Electronic Communications in Probability [electronic only]

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