Feynman-Kac formula for the stochastic heat equation driven by general Gaussian noises

In this talk I will present some results on stochastic heat equations driven by a Gaussian noises. I will focus on Feynman-Kac representation of the solution and the moments of the solution. Both lower and upper bounds for the $$L^p$$ moments of the solution are obtained which is relevant to the so-called intermittency. The Driving Gaussian noises include fractional Brownian fields of Hurst parameters greater or smaller than 1/2.