Stochastic fractional heat equations driven by fractional noises (Q1665638)

Summary: This paper is concerned with the following stochastically fractional heat equation on \((t, x) \in [0, T] \times \mathbb{R}^d\) driven by fractional noise: \(\partial u(t, x) / \partial t = \mathcal{D}_\delta^\alpha u(t, x) + W^H(t, x) \diamond u(t, x)\), where the Hurst parameter \(H = (h_0, h_1, \ldots, h_d)\) and \(\diamond\) denotes the Skorokhod integral. A unique solution of that equation in an appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and the Hölder continuity of the solution on both space and time parameters is discussed. On the other hand, the absolute continuity of the solution is also obtained.