Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

We consider the stochastic heat equation with multiplicative noise in ℝ + ×ℝ d , whose solution is interpreted in the mild sense. The noise is fractional in time (with Hurst index H ≥1/2), and colored in space (with spatial covariance kernel f ). When H >1/2, the equation generalizes the Itô-sense equation for H =1/2. We prove that if f is the Riesz kernel of order α , or the Bessel kernel of order α < d , then the sufficient condition for the existence of the solution is d ≤2+ α (if H >1/2), respectively d