Existence And Uniqueness Of Mild Solution To Fractional Stochastic Heat Equation

For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset D⊂RdD⊂Rd and driven by an L2(D)L2(D)-valued fractional Brownian motion with the Hurst index H>1/2H>1/2, a new result on existence and uniqueness of a mild solution is established. Compared to the existing results, the uniqueness in a fully nonlinear case is shown, not assuming the coefficient in front of the noise to be affine. Additionally, the existence of moments for the solution is established.