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In this article, we consider the stochastic wave and heat equations driven bya Gaussian noise which is spatially homogeneous and behaves in time like afractional Brownian motion with Hurst index $H>1/2$. The solutions of theseequations are interpreted in the Skorohod sense. Using Malliavin calculustechniques, we obtain an upper bound for the moments of order $p\geq2$ of thesolution. In the case of the wave equation, we derive a Feynman-Kac-typeformula for the second moment of the solution, based on the points of a planarPoisson process. This is an extension of the formula given by Dalang, Muellerand Tribe [Trans. Amer. Math. Soc. 360 (2008) 4681-4703], in the case $H=1/2$,and allows us to obtain a lower bound for the second moment of the solution.These results suggest that the moments of the solution grow much faster in thecase of the fractional noise in time than in the case of the white noise intime.

Intermittency for the wave and heat equations with fractional noise in time