Mild solutions for a class of fractional SPDE’s and their sample paths

Abstract. We introduce a notion of mild solution for a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset D ⊂ Rd and driven by an infinite-dimensional frac-tional noise. We prove the existence of such a solution, establish its relation with the variational solution introduced in [42] and also prove the Hölder continuity of its sample paths when we consider it as an L2(D)–valued stochastic process. When h is an affine function, we also prove unique-ness. An immediate consequence of our results is the indistinguishability of mild and variational solutions in the case of uniqueness