FUBINI THEOREM FOR ANTICIPATING STOCHASTIC INTEGRALS IN HILBERT-SPACE

Let (X, C, mu) be a measure space, let W be a cylindrical Hilbert-Wiener process, and let phi be an anticipating integrable process-valued function on X. We prove, under natural assumptions on phi, that there exists a measurable version Y(x), x is-an-element-of X, of the anticipating integral of phi(x) such that the integral integralx Y(x)mu(dx) is a version of the anticipating integral of integral x phi(x)mu(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.