Fubini theorem for anticipating stochastic integrals in Hilbert space

Abstract

Abstract. Let (X, ~, #) be a measure space, let W be a cylindrical HilbertWiener process, and let ~0 be an anticipating integrable process-valued function on X. We prove, under natural assumptions on ~o, that there exists a measurable version Yx, x e X, of the anticipating integral of cp(x) such that the integral ~x Y~#(dx) is a version of the anticipating integral of ~x ~o(x)kt(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.

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