Variational solutions for a class of fractional stochastic partial differential equations

Abstract

In this Note we present new results regarding the existence, the uniqueness and the equivalence of two notions of variational solution related to a class of non autonomous, semilinear, stochastic partial differential equations defined on an open bounded domain D ⊂ R d . The equations we consider are driven by an infinite-dimensional noise derived from an L 2 ( D ) -valued fractional Wiener process W H with Hurst parameter H ∈ ( 1 γ + 1 , 1 ) , where γ ∈ ( 0 , 1 ] denotes the Hölder exponent of the derivative of the nonlinearity that appears in the stochastic term. To cite this article: D. Nualart, P.-A. Vuillermot, C. R. Acad. Sci. Paris, Ser. I 340 (2005).