Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

International audienceWe consider the stochastic heat equation with multiplicative noise $u_t=\frac{1}{2}\Delta u+ u \diamond \dot{W}$ in $\bR_{+} \times \bR^d$, where $\diamond$ denotes the Wick product, and the solution is interpreted in the mild sense. The noise $\dot W$ is fractional in time (with Hurst index $H \geq 1/2$), and colored in space (with spatial covariance kernel $f$). We prove that if $f$ is the Riesz kernel of order $\alpha$, or the Bessel kernel of order $\alpha1/2$), respectively $d