Feynman-Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise

In this paper, we establish a Feynman-Kac formula for the stochastic parabolic Anderson model with Gaussian potential in space and fractional white noise in time with Hurst parameter H > 1/2. We obtain the necesscary and suffcient condition for the integrability of the Gaussian potential and the exponential integrability of the solution which is defined by Feynman-Kac formula. By the smoothing of the fractional white noise and techniques from Malliavin calculus, we prove that the Feynman-Kac representation is a mild solution of the stochastic parabolic Anderson equation.